Ivan Papić
Assistant Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Theoretical and applied probability and statistics
 In particular: diffusions and fractional diffusions
Degrees
 PhD in Mathematics, Faculty of Natural Science, Department of Mathematics, University of Zagreb, 2019
 Thesis: Timechanged stochastic models: fractional Pearson diffusions and delayed continuoustime autoregressive processes, supervisors: N. N. Leonenko, N. Šuvak
 MSc in Mathematics, Financial and Business Mathematics, Department of Mathematics, University of Osijek, Croatia, 2013
 MSc in Mathematics and Computer Science Education, Department of Mathematics, University of Osijek, Croatia, 2020
 BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2011
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.
 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, I. Papić, Correlation properties of continuoustime autoregressive processes delayed by the inverse of the stable subordinator, Communications is Statistics  Theory and Methods 49/20 (2020), 50915113We define the delayed Lévydriven continuoustime autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed nonstationary delayed Lévydriven continuoustime autoregressive processes of order p, emphasising low orders, and we show they exhibit longrange dependence property. Dis tributional properties are discussed as well.
 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.
 N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, EhrenfestBrillouintype correlated continuous time random walk and fractional Jacobi diffusion, Theory of Probability and Mathematical Statistics 99 (2019), 137147Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on EhrenfestBrillouintype 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 nonindependent 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))
 N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli 24/4B (2018), 36033627Continuous 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 urnscheme model and WrightFisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with nonindependent increments. The waiting times are selected from the domain of attraction of a stable law.
 N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Heavytailed fractional Pearson diffusions, Stochastic Processes and their Applications 127/11 (2017), 35123535We define heavytailed fractional reciprocal gamma and FisherSnedecor diffusions by a non Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with spacevarying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and FisherSnedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavytailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and FisherSnedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
 N. Graovac, I. Papić, E. Merdić, Pupil’s DietRelated Attitudes to Healthy Lifestyle, Journal of Environmental Science and Engineering A 4 (2015), 651664The main purpose of this article was to find out more about eating habits along with other habits, attitudes and activities of elementary school pupils. Another aim was to determine possible differences among pupils, depending on their sex, age and environment. Furthermore, based on the anthropometric data (body mass and height) and age, this article was to determine the nutritional status of pupils. The research was conducted via questionnaire constructed for the needs of this specific research. Six hundred and fiftyone pupils took part in this questionnaire in a ratio of 41:59 urban/rural and 51:49 girls/boys. Most of the interviewed pupils (73.88%) have normal body mass according to their age. The share of underweight and overweight pupils is bigger among the boys. Nutritional habits differ among pupils from the urban and rural areas, but they do not differ as much among boys and girls. In addition, their nutritional habits become worse as they grow up.
Refereed Proceedings
 N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Theoretical and simulation results on heavytailed fractional Pearson diffusions, 20th European Young Statisticians Meeting, Uppsala, Sweden, 2017, 95103
Others
 D. Jankov Maširević, I. Papić, Tri klasična problema, Osječki matematički list 12 (2012), 1119
Projects
 Limiting behavior of intermittent processes and diffusions (Granično ponašanje intermitentnih procesa i difuzija; 20182019), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Danijel Grahovac (the project was funded by the J.J. Strossmayer University of Osijek)
 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 Mathematic, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
Grants
 ERASMUS grant for mobility of scientists (study visit to BabesBolyai University, ClujNapoca, Romania, 2016)
 Grant of the AMACUK, United Kingdom Association of Alumni and Friends of Croatian Universities (study visit to School of Mathematics, Cardiff University, UK, 2016)
Professional Activities
Conferences and Workshops
 Workshop on Quantitative Methods for Insurance and Finance, June 56, 2014, Zagreb, Croatia
 6th Croatian Mathematical Congress, June 1417, 2016, Zagreb, Croatia (poster presentation)
 Mathematics for Big Data, May 31  June 1, 2017, Novi Sad, Serbia
 Workshop on Quantitative Modeling in Biomedicine, June 57, 2017, Zagreb, Croatia
 Korean Croatian Summer Probability Camp, July 36, 2017, Zagreb, Croatia
 20th European Young Statisticians Meeting, August 1418, 2017, Uppsala, Sweden (short communication)
 22nd Young Statisticians Meeting, October 1315, 2017, Zagreb, Croatia (short communication)
 The 2nd International Statistical Conference in Croatia, May 1011, 2018, Opatija, Croatia (short communication)
 18th Winter school on Mathematical Finance, January 2123, 2019, Lunteren, Netherlands
 11th International Conference on Extreme Value Analysis, July 15, 2019, Zagreb, Croatia
 32nd European Meeting of Statisticians, July 2226, 2019, Palermo, Italy (poster presentation)
Study Visits
 School of Mathematics, Cardiff University, UK (study visits lasting 2 weeks in February, 3 weeks in November and December 2016 and 2 weeks in November 2017)
Service Activities
 tajnik Statističkog seminara u Osijeku, 2017 
Teaching
Teme završnih i diplomskih radova 2020./2021.
Courses:
 Vjerojatnost i statistika (Probability and Statistics), Faculty of Civil Engineering, University of Osijek (winter semester)
 Statistika (Statistics), Faculty of Education, Undergraduate University Studies of Kinesiology, University of Osijek (winter semester)
 Uvod u vjerojatnost i statistiku (Introduction to Probability and Statistics), Department of Mathematics, University of Osijek (winter semester)
 Primijenjena statistika (Applied statistics), Faculty of Civil Engineering, University of Osijek (winter semester)
 Statistički praktikum (Statistical Lab), Department of Mathematics, University of Osijek (spring semester)
 Slučajni procesi II (Stochastic processes II), Department of Mathematics, University of Osijek (spring semester)
Courses taught:
 Mathematics (Faculty of Economics in Osijek, University of Osijek)
 Mathematics (Faculty of Agriculture in Osijek, University of Osijek)
 Mathematics I (Faculty of Food Technology Osijek, University of Osijek)
 Statistics (Faculty of Food Technology Osijek, University of Osijek)
 Statistics (Department of Mathematics, University of Osijek)
 Numerical Mathematics (Department of Mathematics, University of Osijek)
Konzultacije (Office Hours): Srijeda (Thu): 13:00