Research Interests

• Diffusion processes
• Statistical analysis of stochastic processes

Degrees

• PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2010
• BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2004

Publications

1. N. Šuvak, Time scale transformation in bivariate Pearson diffusions: A shift from light to heavy tails, Axioms 13/11 (2024)
   Abstract

   Heavy-tailed Pearson diffusions provide a natural alternative to well-known Ornstein–Uhlenbeck and Cox–Ingersoll–Ross processes in applications that require addressing heavy-tailed behavior. In this paper, all three heavy-tailed Pearson diffusions, having inverse gamma, Fisher–Snedecor and Student stationary distributions, are constructed via an absolutely continuous time-change process employed in a specific functional transformation of CIR or OU. Moreover, time-change rates in stochastic clocks are continuous functionals of the CIR process.
2. N.N. Leonenko, Ž. Salinger, A. Sikorskii, N. Šuvak, M. Boivin, Generalized Gaussian time series model for increments of EEG data, Statistics and its Interface 16/1 (2023), 17-29
   Abstract

   We propose a new strictly stationary time series model with marginal generalized Gaussian distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram (EEG) data collected from Ugandan children during coma from cerebral malaria. The model inherits its appealing properties from the strictly stationary strong mixing Markovian diffusion with invariant generalized Gaussian distribution (GGD). The GGD parametrization used in this paper comprises some famous light-tailed distributions (e.g., Laplace and Gaussian) and some well known and widely applied heavy-tailed distributions (e.g., Student). Two versions of this model fit to the data from each EEG channel. In the first model, marginal distributions is from the light-tailed GGD sub-family, and the distribution parameters were estimated using quasi-likelihood approach. In the second model, marginal distributions is heavy-tailed (Student), and the tail index was estimated using the approach based on the empirical scaling function. The estimated parameters from models across EEG channels were explored as potential predictors of neurocognitive outcomes of these children 6 months after recovering from illness. Several of these parameters were shown to be important predictors even after controlling for neurocognitive scores immediately following cerebral malaria illness and traditional blood and cerebrospinal fluid biomarkers collected during hospitalization.
3. N.N. Leonenko, A. Sikorskii, Ž. Salinger, M. Boivin, N. Šuvak, Multimodal diffusion model for increments of electroencephalogram data, Stochastic Environmental Research and Risk Assessement 37 (2023)
   Abstract

   We propose a new strictly stationary strong mixing diffusion model with marginal multimodal (three-peak) distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram data collected from Ugandan children during coma from cerebral malaria. We treat the increments as discrete-time observations and construct a diffusion process where the stationary distribution is viewed as a mixture of three non-central generalized Gaussian distributions and we state some important properties related to the moments of this mixture. We estimate the distribution parameters using the expectation-maximization algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and kurtosis. The derived estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. We compare different predictive models and determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction.
4. J. Đorđević, M. Milošević, N. Šuvak, Non-linear stochastic model for dopamine cycle, Chaos, Solitons & Fractals 1 (2023)
   Abstract

   Dopamine is a crucial neurotransmitter that plays a central role in various aspects of brain functions, including reward processing, motivation, learning, and movement control. Its intricate involvement in these biological processes has made it a subject of extensive research across multiple disciplines, ranging from neuroscience and psychology to computational modeling. In this paper the non-linear stochastic model describing synthesis, storage, release, uptake and metabolism of dopamine in dopaminergic nerve terminal of the rat striatum is introduced. The model is driven by 9-dimensional Brownian motion with constant coordinate intensities. Existence and uniqueness of a positive global solution on a corresponding time-domain are proved and lower and upper bounds for specific moments of coordinate processes are derived. These results are used for calculation of bounds for intensities of driving processes and time horizons ensuring that expected values of coordinate processes stay in the same time-interval as the corresponding expected starting values. Furthermore, positivity preserving balance implicit method is used for simulation of coordinate processes in order to illustrate theoretical results.
5. J. Đorđević, I. Papić, N. Šuvak, A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2, Chaos, Solitons & Fractals 148/110991 (2021)
   Abstract

   We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARS-Cov-2, causing the COVID-19 disease, taking into account the spread of the virus due to the regular infected individuals, hospitalized individuals and superspreaders. The model is constructed from the corresponding ordinary differential model by introducing two independent environmental white noises in transmission coefficients for above mentioned classes - one noise for infected and hospitalized individuals and the other for superspreaders. Therefore, the model is defined as a system of stochastic differential equations driven by two independent standard Brownian motions. Existence and uniqueness of the global positive solution is proven, and conditions under which extinction and persistence in mean hold are given. The theoretical results are illustrated via numerical simulations.
6. J. Đorđević, B. Jovanović, J. Manojlović, N. Šuvak, Analysis of stability and sensitivity of deterministic and stochastic models for the spread of new corona virus SARS-CoV-2, Filomat 35/3 (2021), 1045-1063
   Abstract

   Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARS-CoV-2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the disease-free equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and mean-persistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.
7. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology, Journal of Mathematical Analysis and Applications 486/2 (2020)
   Abstract

   Continuous time random walks (CTRWs) have random waiting times between particle jumps. We establish fractional diffusion approximation via correlated CTRWs. Instead of a random walk modeling particle jumps in the classical CTRW model, we use discrete-time Markov chain with correlated steps. The waiting times are selected from the domain of attraction of a stable law.
8. N.N. Leonenko, A.M. Kulik, I. Papić, N. Šuvak, Parameter estimation for non-stationary Fisher-Snedecor diffusion, Methodology and Computing in Applied Probability 22/3 (2020), 1023-1061
   Abstract

   The problem of parameter estimation for the non-stationary ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion, is considered. We propose generalized method of moments (GMM) estimator of unknown parameter, based on continuous-time observations, and prove its consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix in asymptotic normality framework is calculated according to the new iterative technique based on evolutionary equations for the point-wise covariations. The results are illustrated in a simulation study covering various starting distributions and parameter values.
9. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Ehrenfest-Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion, Theory of Probability and Mathematical Statistics 99 (2019), 137-147
   Abstract

   Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not a Lévy process but a diffusion process with non-independent increments. The waiting times between jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with these waiting times converge to Y (E(t))
10. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli 24/4B (2018), 3603-3627
    Abstract

    Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model and Wright-Fisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with non-independent increments. The waiting times are selected from the domain of attraction of a stable law.
11. I. Tolić, K. Miličević, N. Šuvak, I. Biondić, Non-linear Least Squares and Maximum Likelihood Estimation of Probability Density Function of Cross-Border Transmission Losses, IEEE Transactions on Power Systems 33/2 (2018), 2230-2238
    Abstract

    In the modern power system, transmission losses play an increasingly important role in determining the costs of transmission system operators, in particular in cross-border energy exchange. A variety of transmission losses calculation methods are present in scientific literature in recent years, but regularly neglecting the measurement uncertainty which is an important contribution in calculating the final cost of exchanged energy. Due to the significant cost of transmission losses in total costs, all transmission system operators are interested in discovering the probabilistic nature of transmission losses as a fundamental requirement for finding the fair method for transmission losses allocation. In this paper, transmission losses are simulated on 110 kV cross-border transmission line using an Adaptive Monte Carlo method. The probability density estimation procedure is performed by the non-linear least-squares method, using the Levenberg–Marquardt algorithm. The Gaussian, log-normal, Rayleigh, four-parameter beta, generalized trapezoidal and the sum of uniform and normal distribution are fitted and the quality of the distribution estimates is compared according to the corresponding values of the Kolmogorov-Smirnov statistic. Furthermore, an additional example presents a distribution fitting procedure on the zero-impedance data of the same transmission line.
12. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications 127/11 (2017), 3512-3535
    Abstract

    We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non- Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
13. M. Janković, A. Leko, N. Šuvak, Application of lactation models on dairy cow farms, Croatian Operational Research Review 7/2 (2016), 217-227
    Abstract

    One of the most important parts of the contemporary global economy is the food production. Our focus is the milk production on farms of dairy cows, the period in which the cows produce milk (lactation) and the quantity of the milk produced. The special attention will be given to the time-dependent function that describes the quantity of the milk produced over the lactation period. Its graph is known as the lactation curve and it is one of the most important indicators in the dairy farm management. In this paper, we present the time-dependent parametric models for the daily average milk production on one dairy farm. Beside with the well-known Wood's model, the data will be fitted to some less known models such as the MilkBot model and also to the combination of these two models. Model parameters will be interpreted in the framework of the milk production. Finally, we will compare all of the observed models.
14. D. Grahovac, N. Šuvak, Heavy-tailed modeling of CROBEX, Financial Theory and Practice 39/4 (2015), 411-430
    Abstract

    Classical continuous-time stochastic models for log-returns of risky assets, such as the Black-Scholes model, usually assume independence and normality of distributions of log-returns. However, empirical properties of log-returns often show a specific correlation structure and a deviation from normality, in most cases suggesting that their distribution exhibits heavy tails. A natural alternative for modeling log-returns in continuous time would be a stochastic process incorporating a weak form of dependence and a heavy-tailed distribution that is in some way close to the normal distribution. The Student's distribution with small value of tail index (number of degrees of freedom) is the logical choice for such heavy-tailed distribution. Therefore we suggest an alternative continuous-time model for log-returns, a diffusion process with Student's marginal distributions and exponentially decaying autocorrelation structure. This model depends on several unknown parameters that need to be estimated. The tail index is estimated by the method based on the empirical scaling function, while the parameters describing the mean, the variance and the correlation structure of the model are estimated by the generalized method of moments. The model is applied to the CROBEX stock market index, meaning that the estimation of model parameters is based on the CROBEX log-returns. Quality of the proposed model is assessed by the means of simulations, specifically by comparing CROBEX log-returns with the simulated trajectories of the Student's diffusion depending on estimated parameter values.
15. M. Rukav, K. Stražanac, N. Šuvak, Z. Tomljanović, Markov decision processes in minimization of expected costs, Croatian Operational Research Review 5/2 (2014), 247-257
    Abstract

    Basics of Markov decision processes will be introduced in order to obtain the optimization goal function for minimizing the long-run expected cost. We focus on minimization of such cost of the farmer's policy consisting of different decisions in specic states regarding both milk quality and quantity (lactation states) produced by a dairy cow. The transition probability matrix of the Markov process, used here for modeling of transitions of a dairy cow from one state to another, will be estimated from the data simulated from the lactation model that is often used in practice. We want to choose optimal actions in the states of this Markov process regarding the farmer's costs. This problem can be solved by exhaustive enumeration of all possible cases in order to obtain the optimal policy. How- ever, this is feasible only for a small number of states. Generally, this problem can be approached in the linear programming setting which yields an efficient solution. In order to demonstrate and compare these two approaches, we present an example based on the simulated data regarding milk quality and quantity.
16. I. Šandrk Nukić, N. Šuvak, Impact of human resources management on business result of Croatian construction companies, Organization Technology and Management in Construction: an International Journal 5/1 (2013), 663-675
    Abstract

    It has been widely recognized that activities practiced by human resources management (HRM) significantly influence business performance of any company. However, quantifica-tion of that relationship has not been researched enough to provide a tool for practitioners by which they could increase their business result. Therefore additional scientific contri-bution on the subject would be valuable and that is the very purpose of this paper. Authors of this paper have researched what is the impact of HRM activities in construction industry in Croatia. After an insight into a theoretical background about influence of HRM activities on business performance, this paper presents results from their own study. The research was conducted over actual financial results realised before and during the period of recent economic crisis, from 2007-2010. Data was collected using financial data base Poslovna.hr and the opinion poll conducted in more than 30% of middle-size construction companies in Croatia. Data was analysed using frequency analysis, analysis of correlation coefficients and finally by construction of multi-ple linear regression models. Results of the research suggest that people working in construc-tion have reached the subsistence level income. Constructed multiple linear regression models indicate that, among other human resources activities, the material motivation activities have the most significant positive impact on business result. Professional selection of candidates, life long learning, sup-portive organizational culture and other non-material measures remain for the benefit of some future times.
17. F. Avram, N.N. Leonenko, N. Šuvak, On spectral analysis of heavy-tailed Kolmogorov-Pearson diffusions, Markov Processes and Related Fields 19/2 (2013), 249-298
    Abstract

    The self-adjointness of the semigroup generator of one dimensional diffusions implies a spectral representation (see [33, 50]) which has found many useful applications, for example for the prediction of second order stationary sequences (see [18]) and in mathematical finance (see [47]). However, on noncompact state spaces the spectrum of the generator will typically include both a discrete and a continuous part, with the latter starting at a spectral cutoff point related to the nonexistence of stationary moments. The significance of this fact for statistical estimation is not yet fully understood. We consider here the problem of spectral representation of transition density for an interesting class of examples: the hypergeometric diffusions with heavytailed Pearson type invariant distribution of a) reciprocal (inverse) gamma, b) Fisher – Snedecor, or c) skew-Student type. As opposed to the “classic” hypergeometric diffusions (Ornstein – Uhlebeck, Gamma/CIR, Beta/Jacobi), these diffusions have a continuum spectrum, whose spectral cutoff and transition density we present in this paper.
18. F. Avram, N.N. Leonenko, N. Šuvak, Spectral representation of transition density of Fisher-Snedecor diffusion, Stochastics - An International Journal of Probability and Stochastics Processes 85/2 (2013), 346-369
    Abstract

    We analyse spectral properties of an ergodic heavy-tailed diffusion with the Fisher–Snedecor invariant distribution and compute spectral representation of its transition density. The spectral representation is given in terms of a sum involving finitely many eigenvalues and eigenfunctions (Fisher–Snedecor orthogonal polynomials) and an integral over the absolutely continuous spectrum of the corresponding Sturm– Liouville operator. This result enables the computation of the two-dimensional density of the Fisher–Snedecor diffusion as well as calculation of moments of the form E[X^{;m};X^{;n};], where m and n are at most equal to the number of Fisher– Snedecor polynomials. This result is particularly important for explicit calculations associated with this process.
19. I. Šandrk Nukić, N. Šuvak, Utjecaj upravljanja ljudskim potencijalima na percepciju organizacijske uspješnosti u hrvatskim građevinskim poduzećima, Poslovna izvrsnost 7/2 (2013), 125-141
    Abstract

    Uspjeh poslovanja predstavlja kompleksan pojam koji nije dovoljno analizirati samo financijskim nego i kvalitativnim pokazateljima (Vrdoljak Raguž, 2010). Naime, financijski pokazatelji ukazuju na uspjeh u prošlim razdobljima, dok kvalitativni pokazatelji opisuju utjecaj nematerijalnih varijabli na sposobnost poduzeća da se prilagođava nadolazećim promjenama u okolini. S obzirom na to da su zaposlenici nositelji tih nematerijalnih varijabli, upravljanje ljudskim potencijalima (ULJP) postaje središnje pitanje uspješnosti poslovanja. Fokus ovog rada bio je istražiti odnos relevantnih aktivnosti ULJP s odabranim kvalitativnim pokazateljem – percepcijom organizacijske uspješnosti stručnjaka za ljudske potencijale. Empirijsko istraživanje provedeno je na uzorku više od trećine srednje velikih građevinskih poduzeća u Republici Hrvatskoj. Prikupljeni podaci opisani su korištenjem standardnih mjera deskriptivne statistke. Posebno ističemo zaključivanje o zavisnosti među varijablama na temelju procjena koeficijenata korelacije. U svrhu izgradnje statističkih modela korištena je višestruka linearna regresija. Rezultati istraživanja pokazali su da percepcija organizacijske uspješnosti najviše ovisi: - o primjerenosti, kvaliteti i količini edukacija za zaposlenike, - o načinu pohranjivanja poslovnih informacija i njihovu pristupu, - o učinkovitosti usvajanja znanja od partnera. Budući da je ULJP u Republici Hrvatskoj na relativno niskoj razini i dosadašnja istraživanja pokazuju da na tom području treba još raditi (Pološki Vokić i Vidović, 2008). Ovim radom nastojao se dati znanstveni doprinos transformaciji ULJP-a iz operativnog u strateški poslovni alat.
20. N. Šuvak, N.N. Leonenko, F. Avram, Hypothesis testing for Fisher-Snedecor diffusion, Journal of Statistical Planning and Inference 8/142 (2012), 2308-2321
    Abstract

    We consider the problem of testing the hypothesis whether the random variable X_t, for fixed t grether that zero, on marginal distribution of ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion. We propose a GMM approach to testing this statistical hypothesis where the moment condition is based on eigenfunctions of the diffusion infinitesimal generator - Fisher-Snedecor polynomials. Statistical test is observed in two different settings: 1) for known values of parameters of the process ; 2) for consistent moment based estimators of parameters. Results are illustrated in a short simulation study.
21. I. Đurđević, A. Mirković Moguš, N. Šuvak, Impact of students' activities in a virtual learning environment on their final grade, Active Learning in Higher Education 13 (2012), 177-189
    Abstract

    By studying the use of a virtual learning environment, many have focused on automatically logged web data in order to detect factors that enhance students’ use of the virtual learning environment and that may impact their productive and efficient learning via this means. Following their footsteps, the aim of this research is to examine data (activity logs) obtained by students’ while they are logged into the virtual learning environment in order to detect frequencies and priorities of students’ choice of activities in a virtual learning environment. The activity logs are used to measure students’ effectiveness of learning to determine whether students’ activity logs, within courses supported by a virtual learning environment as part of a blended learning approach, correlate with their final marks and the students’ perceptions of using the virtual learning environment. Observed activities involved course view, assignment view, resource view, forum view, assignment upload and project upload when seen against their final mark. Data log features of a virtual learning environment and an instrument used to gather data on the students’ perceptions of using the virtual learning environment were used. Results show that there are positive correlations between students’ logs of particular activities and their final mark.
22. N.N. Leonenko, L. Sakhno, N. Šuvak, Parameter estimation for reciprocal gamma Ornstein-Uhlenbeck type processes, Theory of Probability and Mathematical Statistics 86 (2012), 137-154
    Abstract

    We consider parameter estimation for a process of Ornstein–Uhlenbeck type with reciprocal gamma marginal distribution, to be called reciprocal gamma Ornstein–Uhlenbeck (RGOU) process. We derive minimum contrast estimators of unknown parameters based on both the discrete and the continuous observations from the process as well as moments based estimators based on discrete observations. We prove that proposed estimators are consistent and asymptotically normal. The explicit forms of the asymptotic covariance matrices are determined by using the higher order spectral densities and cumulants of the RGOU process.
23. F. Avram, N.N. Leonenko, N. Šuvak, Parameter estimation for Fisher-Snedecor diffusion, Statistics - a Journal of Theoretical and Applied Statistics 45/1 (2011), 27-42
    Abstract

    We consider the problem of parameter estimation for an ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher- Snedecor diffusion. We propose moments based estimators of unknown parameters, based on both discrete and continuous observations, and prove their consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix is determined by using the properties of eigenfunctions (Fisher-Snedecor polynomials) of the corresponding Sturm-Liouville operator.
24. N.N. Leonenko, N. Šuvak, Statistical inference for reciprocal gamma diffusion process, Journal of Statistical Planning and Inference 140/1 (2010), 30-51
    Abstract

    We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite sum over the discrete spectrum and an integral over the essential spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.
25. N.N. Leonenko, N. Šuvak, Statistical inference for Student diffusion process, Stochastic Analysis and Applications 28/6 (2010), 972-1002
    Abstract

    We consider the problem of parameter estimation for an ergodic diffusion with symmetric scaled Student invariant distribution. Spectral representation of transition density of such a Markov process is given in terms of a finite sum over the discrete spectrum and an integral over the essential spectrum of the negative infinitesimal generator of Student diffusion. Consistency and asymptotic normality of proposed estimators are presented. Based on the Stein equation for Student diffusion and Routh- Romanovski polynomials, the hypothesis testing procedure is considered.

1. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Theoretical and simulation results on heavy-tailed fractional Pearson diffusions, 20th European Young Statisticians Meeting, Uppsala, Sweden, 2017, 95-103
2. F. Avram, N.N. Leonenko, N. Šuvak, On spectral analysis of heavy-tailed Kolmogorov - Pearson diffusions, The Pyrenees International Workshop on Statistics, Probability and OR, Jaca, Spain, 2012, 33-42
3. I. Đurđević, A. Mirković Moguš, N. Šuvak, Validation of the online learning efficacy through course evaluation, 2nd Special Focus Symposium on IKS: Information and Knowledge Systems, Zagreb, Croatia, 2010, 147-157
4. N.N. Leonenko, N. Šuvak, Parameter estimation for reciprocal gamma and Student diffusion processes, 16th European Young Statisticians Meeting, Bucharest, Romania, 2009, 95-99

1. J. Kraševac, I. Papić, N. Šuvak, Statistička olimpijada, brošura s primjerima riješenih zadataka (2018)
2. N. Šuvak, Hardy-Weinbergov model ravnoteže, Osječki matematički list 5/2 (2005), 91-99
   Abstract

   Ovim člankom, koji je gradivom i pristupom prilagođen četvrtim razredima srednjih škola koje u nastavi matematike imaju teoriju vjerojatnosti, pokušat ćemo kroz zanimljive genetičke činjenice predstaviti upotrebu osnovnog matematičkog aparata teorije vjerojatnosti. S matematičke točke gledišta obradit ćemo model ravnoteže u populaciji do kojeg su neovisno došli britanski matematičar G. H. Hardy (1877.-1947.) i njemački fizičar W. Weinberg (1862.-1937.), te na nekoliko primjera ilustrirati upotrebu ovog modela.

1. M. Benšić, N. Šuvak, Uvod u vjerojatnost i statistiku, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2014.
2. M. Benšić, N. Šuvak, Primijenjena statistika, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2013.

Projects

• Scaling in stochastic models (IP-2022-10-808, December 15, 2023. – December 14, 2027),  project funded by Croatian Science Foundation, Principal investigator: Danijel Grahovac
• COST action CA21169 – Information, Coding, and Biological Function: the Dynamics of Life (DYNALIFE, September 19, 2022 – September 19, 2026), member of WG1, WG2 and WG3
• Application of short-range and long-range dependent stochastic models (bilateral project with Faculty of Natural Sciences – Department of Mathematics, University of Niš, Serbia; Principal investigators: Nenad Šuvak (University of Osijek) and Jasmina Đorđević (University of Niš); Project funded by Ministry of Science and Education of the Republic of Croatia and Ministry of Education, Science and Technology Development of the Republic of Serbia)
• Limiting behavior of intermittent processes and diffusions (2019/2020; Department of Mathematics, University of Osijek; Principal investigator: Danijel Grahovac; Project funded by University of Osijek)
• RealForAll – Real-time measurements and forecasting for successful prevention and management of seasonal allergies in Croatia-Serbia cross-border region (2017 – 2019, Department of Mathematics, University of Osijek; Project ID: HR-RS151)
• Stochastic models with long-range dependence (2017-2018; Department of Mathematics, University of Osijek; Principal investigator: Nenad Šuvak; Project funded by University of Osijek)
• Fractional Pearson Diffusions (2015-2016; Department of Mathematics, University of Osijek; Principal investigator: Nenad Šuvak; Project funded by University of Osijek)
• Statistical Aspects of Parameter Estimation in Nonlinear Parametric Models (2007-2013); Department of Mathematics, University of Osijek; Principal investigator: Prof. M. Benšić; Project funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
• Models for Risk Assessment of the Company (2007-2013; Faculty of Economics, University of Osijek; Principal investigator: Prof. N. Šarlija; Project funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
• Statistical Analysis of Diffusion Processes and their Applications in Economics and Finance (2009-2010; Collaborative project with Prof. Nikolai N. Leonenko from School of Mathematics, Cardiff University, UK; Project funded by the Croatian Science Foundation within the program for education of PhD students)

GRANTS

• ERASMUS grant (study visit to Babes-Bolyai University, Cluj-Napoca, Romania, 2016)
• ERASMUS grant (study visit to School of Mathematics, Cardiff University, UK, 2013)
• Grant of the AMAC-UK, United Kingdom Association of Alumni and Friends of Croatian Universities (study visit to School of Mathematics, Cardiff University, UK, 2011)
• Grant of the Croatian Ministry of Science, Education and Sports for specialization of Croatian PhD students at the foreign Universities (study visit to School of Mathematics, Cardiff University, UK, 2008)

Study visits

• School of Mathematics, Cardiff University, UK (study visits lasting 2-6 weeks in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2016 and 2018)

Professional Activities

Committee Memberships

• 28th Young Statisticians Meeting, October 27-29, 2024, Gödöllő, Hungary
  Member of the International Program Committee
• 27th Young Statisticians Meeting, September 29 October 1, 2023, Osijek, Croatia
  Member of the International Program Committee
• 26th Young Statisticians Meeting, September 30 – October 2, 2022, Bohinj, Slovenia
  Member of the International Program Committee
• “Innovative Teaching of Mathematics” – National Meeting of Math Teachers, 25-26 August 2022, Osijek, Croatia
  Member of the Organizing Committee
• 25th Young Statisticians Meeting, 15-17 October 2021, Monichwald/Vorau, Austria
  Member of the International Program Committee
• “Innovative Teaching of Mathematics” – National Meeting of Math Teachers, 27-28 August 2020, Osijek, Croatia
  Chair of the Organizing Committee
• 24th Young Statisticians Meeting, 18-20 October 2019, Basovizza, Italy
  Member of the International Program Committee
• 21st European Young Statisticians Meeting, July 29 – August 2, 2019, Belgrade, Serbia
  Member of the International Organizing Committee/Scientific Program Committee
• 23rd Young Statisticians Meeting, 12-14 October 2018, Balatonfured, Hungary
  Member of the International Program Committee
• “Innovative Teaching of Mathematics” – National Meeting of Math Teachers, 30-31 August 2018, Osijek, Croatia
  Chair of the Organizing Committee
• “Innovative Teaching of Mathematics” – National Meeting of Math Teachers, 25-26 August 2016, Osijek, Croatia
  Chair of the Organizing Committee/Scientific Program Committee
• 18th European Young Statisticians Meeting, 26-30 August 2013, Osijek, Croatia
  Chair of the Local Organizing Committee
• 17th European Young Statisticians Meeting, 5-9 September 2011, Lisbon, Portugal
  Member of the International Organizing Committee/Scientific Program Committee

Refereeing

• Scientific journals: Mathematical Communications, Glasnik matematički, Random Operators and Stochastic Equations, Journal of Classical Analysis, International Journal of Stochastic Analysis, Communication in Statistics – Simulation and Computation, Physical Communication, International Journal of Applied and Computational Mathematics, Mathematics, Applied Mathematical Modelling, Journal of Biological Physics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Applied Probability Journals
• Professional journals: Osijek Mathematical Gazette

Reviewing

• AMS Mathematical Reviews (2011-2020)

Service Activities

• President of the Osijek Mathematical Society (2017-2021)
• Co-chair of the Statistical seminar, School of Applied Mathematics and Informatics (since January 2017)
• Member of the Higher Education Quality Assurance Board, School of Applied Mathematics and Informatics (since 2006)

Conferences and Workshops

• Functional Analysis IX, June 2005, Dubrovnik, Croatia
• 4th Croatian Mathematical Congress, June 17– 21, 2008, Osijek, Croatia (short communication)
• 13th Young Statisticians Meeting, October 16–18, 2008, Balatonfured, Hungary (short communication)
• Croatian Quants Day, April 17, 2009, Department of Mathematics, Zagreb
• 16th European Young Statisticians Meeting, August 24-28, 2009, Bucharest, Romania (short communication)
• Workshop on Modern Interdisciplinary Applications of Powerful Techicques in Statistics (focus on Singular Spectrum Analysis (SSA) method), December 1, 2009, School of Mathematics, Cardiff University, Cardiff, UK
• High-Dimensional Data Analysis in Economics Workshop, May 19-20, 2010, Faculty of Economics, University of Zagreb, Croatia
• Croatian Quants Day, April 9, 2010, Department of Mathematics, Zagreb
• International Symposium on Business and Industrial Statistics, July 5 – 9, 2010, Portorose, Slovenia (invited speaker)
• Summer School in Financial Mathematics, August 22 – September 2, 2011, Ljubljana, Slovenia
• Statistical Analysis of Financial Data Workshop, September 30 – October 1, 2011, Opatija, Croatia (invited speaker)
• Spring School in Probability, April 23-27, 2012, Dubrovnik, Croatia
• Croatian Quants Day, May 11, 2012, Department of Mathematics, Zagreb
• Workshop “Modern Trends in Markov Processes and Queuing Theory”, February 15, 2013, Welsh Institute of Mathematical and Computational Sciences, Cardiff, UK (short communication)
• 18th European Young Statisticians Meeting, August 26-30, 2013, Osijek, Croatia
• Workshop on Quantitative Methods for Insurance and Finance, June 5-6, 2014, Zagreb, Croatia
• 15th International Conference on Operational Research KOI 2014, September 24-26, 2014, Osijek, Croatia (short communication)
• 38th Conference on Stochastic Processes and their Applications, July 13-17, 2015, University of Oxford, UK (short communication)
• 6th Croatian Mathematical Congress, June 14-17, 2016, Zagreb, Croatia (short communication)
• 16th Conference on Operational Research KOI2016, September 27-29, 2016, Osijek, Croatia (short communication)
• Mathematics for Big Data, May 31 – June 1, 2017, Novi Sad, Serbia
• Korean Croatian Summer Probability Camp, July 3-6, 2017, Zagreb, Croatia
• 39th Conference on Stochastic Processes and their Applications, July 24-28, 2017, Moscow, Russia (short communication)
• 21st European Young Statisticians Meeting, 14-18 August 2017, Uppsala, Sweden (short communication with Ivan Papić)
• 22nd Young Statisticians Meeting, October 13-15, 2017. Zagreb, Croatia (short communication with Ivan Papić)
• ISSCRO’18 (2nd International Statistical Conference in Croatia), May 10-11, Opatija, Croatia
• 32nd European Meeting of Statisticians, July 22-26, 2019, Palermo, Italy (short communication)
• ESPID – European Society for Paediatric Infectious Diseases, 39th Annual MeetingESPID – European Society for Paediatric Infectious Diseases, 39th Annual Meeting, Online Meeting and Hosted from Geneva, May 24-29, 2021 (short communication with Ivana Valenčak Ignjatić, Universitiy Hospital for Infectious Diseases “Dr. Fran Mihaljević”, Department for Pediatric Infectious Diseases, Zagreb, Croatia)
• 22th European Young Statisticians Meeting, September 6-10, 2021, Greece (organized online, short communication with Željka Salinger)
• 25th Young Statisticians Meeting, October 15-17, 2021, Monichwald/Vorau, Austria (short communication with Željka Salinger)
• 7th Croatian Mathematical Congress, June 15-18, 2022, Split, Croatia (short communication)
• STORM Workshop, September 5-8, 2022, Oslo, Norway (invited lecture)
• 12th Symposium Mathematics and Applications, December 2-3, 2022, Belgrade, Serbia (invited lecture)
• 19th International Conference Applied Statistics 2023, September 24-26, 2023, Koper, Slovenia (short communication)
• 27th Young Statisticians Meeting, September 29 – October 1, 2023, Osijek, Croatia (organizer)
• Bioinference, June 5-7, 2024, Warwick University, UK (short communication)
• 8th Croatian Mathematical Congress, July 2-5, 2024, Osijek, Croatia (short communication)
• CSTAT Summer School (organized by Computational Statistics Research Group, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology), October 17-18, 2024, St. Lorenzen am Wechsel, Austria (short communication)
• 28th Young Statisticians Meeting, October 27-29, 2024, Gödöllő, Croatia (member of the International Program Committee)

Lectures and Seminar talks

• Stohastički integral i Itova formula, Seminar za teoriju vjerojatnosti, PMF-Matematički odjel, Zagreb, 2. i 9. svibnja 2006.
• Dokazi nepotpunosti bez dijagonalne leme, Seminar za logiku i osnove matematike, PMF-Matematički odjel, Zagreb, 3. travnja 2007.
• Statistical analysis of Pearson diffusions with heavy-tailed marginal distributions, OR and Statistics Seminar, School of Mathematics, Cardiff University, UK, November 10, 2009
• Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove, Seminar za optimizaciju i primjene, Odjel za matematiku, Osijek, 16. prosinca 2009.
• Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove I, II, III, Seminar za teoriju vjerojatnosti, PMF-Matematički odjel, Zagreb, 16. i 23. veljače, 30. ožujka 2010.
• Testiranje hipoteza za Fisher-Snedecorovu difuziju, Matematički kolokvij, Odjel za matematiku, Osijek, 19. travnja 2012.
• Bertrandov paradoks – nastavni izazovi, Geometrijska škola Stanka Bilinskog, SŠ Isidora Kršnjavoga, Našice, 8. travnja 2017.
• Mjere zavisnosti – svojstva i zamke, Statistički seminar, Odjel za matematiku, Osijek, 14. prosinca 2017.
• Modeliranje koncentracije peludi ambrozije, Statistički seminar, Odjel za matematiku, Osijek, 8. studenog 2018.
• Statistical analysis of Pearson diffusions with heavy-tailed marginal distributions, Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Niš, Serbia, February 14, 2020.
• Stochastic models for SARS-CoV-2 epidemics, Statistički seminar, Odjel za matematiku, Osijek, February 3, 2022.

Teaching

Konzultacije (Office Hours)

• po dogovoru e-mailom ili putem MS Teams platforme

Teme završnih i diplomskih radova

• teme završnih radova (ak. god. 2023./2024.)
• teme diplomskih radova (ak. god. 2023./2024.)

Courses

• Matematičke financije (Mathematical Finance), School of Applied Mathematics and Informatics, University of Osijek (winter semester)
• Slučajni procesi II (Stochastic Processes II), School of Applied Mathematics and Informatics, University of Osijek (spring semester)
• Stručna praksa (Professional practice), School of Applied Mathematics and Informatics, University of Osijek
• Primijenjena i inženjerska matematika (Applied and Engineering Mathematics), Faculty of Food Technology, University of Osijek
• Matematika i statistika (Mathematics and Statistics, mandatory PhD course), Mechanical Engineering Faculty, University of Slavonski Brod

Courses taught

• Selected Applications of Probability, Stochastic Processes I, Probability, Introduction to Probability and Statistics, StatLab, Elementary Mathematics I and II, Introduction to Probability and Statistics, Introduction to Computer Science, Web Programming (School of Applied Mathematics and Informatics, University of Osijek)
• Mathematics IV (Department of Physics, University of Osijek)
• Statistics (Faculty of Education, University of Osijek)
• Mathematics (Faculty of Agriculture, University of Osijek)
• Probability and Statistics (Faculty of Civil Engineering,  University of Osijek)
• Statistics (Faculty of Food Technology, University of Osijek)