Ivan Papić

 

 AVM6240  PhD
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-812
fax: +385-31-224-801
email: ipapic @ mathos.hr
office:  14 (first floor)

 


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: Time-changed stochastic models: fractional Pearson diffusions and delayed continuous-time autoregressive processes, supervisors: N. N. Leonenko, N. Šuvak
MSc in Mathematics, Financial and Business Mathematics, Department of Mathematics, University of Osijek, Croatia, 2013
BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2011
 

Publications

 
Journal Publications

  1. 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 (2019), prihvaćen za objavljivanje
    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.
  2. 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.
  3. 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 99/2 (2018), 123-133
    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))
  4. 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.
  5. 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. 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. D. Jankov Maširević, I. Papić, Tri klasična problema, Osječki matematički list 12 (2012), 11-19



Projects

  • 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)

Grants

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


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


Teaching

Courses:

  • Matematika I (Mathematics I), Faculty of Food Technology Osijek, University of Osijek (winter semester) 
  • Vjerojatnost i statistika (Probability and Statistics), Faculty of Civil Engineering, University of Osijek (winter semester)
  • Uvod u vjerojatnost i statistiku (Introduction to Probability and Statistics), Department of Mathematics, University of Osijek (winter/spring 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)
  • 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): 

Za vrijeme ispitnih rokova konzultacije se održavaju po dogovoru.