Associate Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia
 phone: +385-31-224-821 fax: +385-31-224-801 email: nsuvak @ mathos.hr office: 18 (first floor)

## 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

Journal Publications

1. 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)
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.
2. 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 (2021), prihvaćen za objavljivanje
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.
3. 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 (2021), prihvaćen za objavljivanje
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.
4. 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)
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.
5. 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
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.

## Projects

Participation (as researcher) in work of the following projects:

• Application of short-range and long-range dependent stochastic models (bilateral project with Faculty of Natural Sciences - Department of Mathematics, University of Niš, Serbia; Project leaders: 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
Project runs in academic year 2019/2020. Project leader: 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, project ID: HR-RS151)

• Stochastic models with long-range dependence (Stohastički modeli s dugoročnom zavisnošću; 2017-2018), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
• Fractional Pearson Diffusions (Frakcionalne Pearsonove difuzije; 2015-2016), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
• Statistical Aspects of Parameter Estimation in Nonlinear Parametric Models (Statistički aspekti procjene parametara u nelinearnim parametarskim modelima; 2007-2013), Department of Mathematic, University of Osijek, Leader: Prof. M. Benšić (the project was funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
• Models for Risk Assessment of the Company (Modeli za ocjenu rizičnosti poslovanja poduzeća; 2007-2013), Faculty of Economics, University of Osijek, Leader: Prof. N. Šarlija (the project was 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) - this project was a collaborative project with Professor Nikolai N. Leonenko from School of Mathematics, Cardiff University, UK (the project was funded by the Croatian Science Foundation within the program for education of PhD students)

## Grants

• ERASMUS grant for mobility of scientists (study visit to Babes-Bolyai University, Cluj-Napoca, Romania, 2016)
• ERASMUS grant for mobility of scientists (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)

## Professional Activities

Committee Memberships

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
• Proffesional journals:
• Osijek Mathematical Gazette

Reviewing

• AMS Mathematical Reviews (2011-2020)

Conferences and Workshops

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.

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)

Service Activities

• President of the Osijek Mathematical Society (since 2017)
• Co-chair of the Statistical seminar of the Department of Mathematics (since January 2017)
• Member of the Higher Education Quality Assurance Board at the Department of Mathematics (since 2006)

## Teaching

Konzultacije (Office Hours):

• Utorkom od 10:00 sati na fakultetu
• Online po dogovoru

Teme završnih i diplomskih radova:

Courses:

Courses taught:

• Probability, Introduction to Probability and Statistics, StatLab, Elementary Mathematics I and II, Introduction to Probability and Statistics, Introduction to Computer Science, Web Programming (Department of Mathematics, 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)