Asisstant Professor

### Ivan Papić

ipapic@unios.hr
14 (1st floor)
School of Applied Mathematics and Informatics

Josip Juraj Strossmayer University of Osijek

### Research Interests

• Diffusions and fractional diffusions
• Time-changed stochastic models
• Applied probability and statistics

### 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. 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.
3. N.N. Leonenko, I. Papić, Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator, Communications is Statistics - Theory and Methods 49/20 (2020), 5091-5113
We define the delayed Lévy-driven continuous-time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed Lévy-driven continuous-time autoregressive processes of order p, emphasising low orders, and we show they exhibit long-range dependence property. Dis- tributional properties are discussed as well.
4. 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.
5. 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
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))
6. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli 24/4B (2018), 3603-3627
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.
7. N.N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications 127/11 (2017), 3512-3535
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.
8. N. Graovac, I. Papić, E. Merdić, Pupil’s Diet-Related Attitudes to Healthy Lifestyle, Journal of Environmental Science and Engineering A 4 (2015), 651-664
The 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 fifty-one 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

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

Others

1. J. Kraševac, I. Papić, N. Šuvak, Statistička olimpijada, brošura s primjerima riješenih zadataka (2018)
2. D. Jankov Maširević, I. Papić, Tri klasična problema, Osječki matematički list 12 (2012), 11-19

### Projects

• Scaling in stochastic models (2023-2027); Project leader: Danijel Grahovac; Project funded by Croatian Science Foundation.
• Application of short-range and long-range dependent stochastic models (2019-2022) (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 (Granično ponašanje intermitentnih procesa i difuzija; 2018-2019), 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 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 Mathematic, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)

### Teaching

• Konzultacije (Office Hours):  Četvrtak, 14:00h. Za vrijeme ispitnih rokova po dogovoru.
• Teme završnih i diplomskih radova 2023/2024: (pdf)
• Courses:
• Vjerojatnost i statistika (Probability and Statistics), Faculty of Civil Engineering, University of Osijek (winter semester)
• Primijenjena statistika (Applied Statistics), Faculty of Ciliv Engineering, University of Osijek (winter semester)
• Uvod u vjerojatnost i statistiku (Introduction to Probability and Statistics), Department of Mathematics, University of Osijek (winter semester)
• Slučajni procesi I (Stochastic processes I), Department of Mathematics, University of Osijek (winter semester)
• Statistički praktikum (Statistical Lab), 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 Education, Undergraduate University Studies of Kinesiology, University of Osijek)
• Statistics (Faculty of Food Technology Osijek, University of Osijek)
• Statistics (Department of Mathematics, University of Osijek)
• Stochastic processes II (Department of Mathematics, University of Osijek)
• Numerical Mathematics (Department of Mathematics, University of Osijek)
• Differential calculus (Department of Mathematics, University of Osijek)
• Differential calculus (Department of Physics, University of Osijek)