Nenad Šuvak
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia

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
 J. Đorđević, I. Papić, N. Šuvak, A two diffusion stochastic model for the spread of the new corona virus SARSCoV2, Chaos, Solitons & Fractals 148/110991 (2021)We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARSCov2, causing the COVID19 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.
 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 SARSCoV2, Filomat (2021), prihvaćen za objavljivanjeBasic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARSCoV2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the diseasefree 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 meanpersistence 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.
 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 objavljivanjeWe 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 lighttailed distributions (e.g., Laplace and Gaussian) and some well known and widely applied heavytailed 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 lighttailed GGD subfamily, and the distribution parameters were estimated using quasilikelihood approach. In the second model, marginal distributions is heavytailed (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.
 N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Approximation of heavytailed 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 discretetime Markov chain with correlated steps. The waiting times are selected from the domain of attraction of a stable law.
 N.N. Leonenko, A.M. Kulik, I. Papić, N. Šuvak, Parameter estimation for nonstationary FisherSnedecor diffusion, Methodology and Computing in Applied Probability 22/3 (2020), 10231061The problem of parameter estimation for the nonstationary ergodic diffusion with FisherSnedecor invariant distribution, to be called FisherSnedecor diffusion, is considered. We propose generalized method of moments (GMM) estimator of unknown parameter, based on continuoustime 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 pointwise 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 shortrange and longrange 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  Realtime measurements and forecasting for successful prevention and management of seasonal allergies in CroatiaSerbia crossborder region (2017  2019, project ID: HRRS151)
 Stochastic models with longrange dependence (Stohastički modeli s dugoročnom zavisnošću; 20172018), 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; 20152016), 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; 20072013), 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; 20072013), 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 (20092010)  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 BabesBolyai University, ClujNapoca, Romania, 2016)
 ERASMUS grant for mobility of scientists (study visit to School of Mathematics, Cardiff University, UK, 2013)
 Grant of the AMACUK, 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
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2728 August 2020, Osijek, Croatia
 Chair of the Organizing Committee
 24th Young Statisticians Meeting, 1820 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, 1214 October 2018, Balatonfured, Hungary
 Member of the International Program Committee
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 3031 August 2018, Osijek, Croatia
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2526 August 2016, Osijek, Croatia
 Chair of the Organizing Committee/Scientific Program Committee
 18th European Young Statisticians Meeting, 2630 August 2013, Osijek, Croatia
 Chair of the Local Organizing Committee
 17th European Young Statisticians Meeting, 59 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
 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 (20112020)
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 2428, 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
 "HighDimensional Data Analysis in Economics" Workshop, May 1920, 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 2327, 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 2630, 2013, Osijek, Croatia
 Workshop on Quantitative Methods for Insurance and Finance, June 56, 2014, Zagreb, Croatia
 15th International Conference on Operational Research KOI 2014, September 2426, 2014, Osijek, Croatia (short communication)
 38th Conference on Stochastic Processes and their Applications, July 1317, 2015, University of Oxford, UK (short communication)
 6th Croatian Mathematical Congress, June 1417, 2016, Zagreb, Croatia (short communication)
 16th Conference on Operational Research KOI2016, September 2729, 2016, Osijek, Croatia (short communication)
 Mathematics for Big Data, May 31  June 1, 2017, Novi Sad, Serbia
 Korean Croatian Summer Probability Camp, July 36, 2017, Zagreb, Croatia
 39th Conference on Stochastic Processes and their Applications, July 2428, 2017, Moscow, Russia (short communication)
 22nd Young Statisticians Meeting, October 1315, 2017. Zagreb, Croatia
 ISSCRO'18 (2nd International Statistical Conference in Croatia), May 1011, Opatija, Croatia
 32nd European Meeting of Statisticians, July 2226, 2019, Palermo, Italy
Lectures and Seminar talks
 Stohastički integral i Itova formula, Seminar za teoriju vjerojatnosti, PMFMatematički odjel, Zagreb, 2. i 9. svibnja 2006.
 Dokazi nepotpunosti bez dijagonalne leme, Seminar za logiku i osnove matematike, PMFMatematički odjel, Zagreb, 3. travnja 2007.
 Statistical analysis of Pearson diffusions with heavytailed 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, PMFMatematički odjel, Zagreb, 16. i 23. veljače, 30. ožujka 2010.
 Testiranje hipoteza za FisherSnedecorovu 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 heavytailed 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 26 weeks in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2016 and 2018)
Service Activities
 President of the Osijek Mathematical Society (since 2017)
 Cochair 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:
 Slučajni procesi I (Stochastic Processes I), Department of Mathematics, University of Osijek (winter semester)
 Slučajni procesi II (Stochastic Processes II), Department of Mathematics, University of Osijek (spring semester)
 Matematičke financije (Mathematical Finance), Department of Mathematics, University of Osijek (winter semester)
 Statistički praktikum (StatLab), Department of Mathematics, University of Osijek (spring semester)
 Stručna praksa (Professional practice), Department of Mathematics, University of Osijek
 Matematika i statistika (Mathematics and Statistics), Mechanical Engineering Faculty, University of Slavonski Brod
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)