Nenad Šuvak

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

Google Scholar

Journal Publications

  1. N.N. Leonenko, A.M. Kulik, I. Papić, N. Šuvak, Parameter estimation for non-stationary Fisher-Snedecor diffusion, Methodology and Computing in Applied Probability (2019), prihvaćen za objavljivanje
    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.
  2. 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.
  3. 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 99/2 (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. I. Tolić, K. Miličević, N. Šuvak, I. Biondić, Non-linear Least Squares and Maximum Likelihood Estimation of Probability Density Function of Cross-Border Transmission Losses, IEEE Transactions on Power Systems 33/2 (2018), 2230-2238
    In the modern power system, transmission losses play an increasingly important role in determining the costs of transmission system operators, in particular in cross-border energy exchange. A variety of transmission losses calculation methods are present in scientific literature in recent years, but regularly neglecting the measurement uncertainty which is an important contribution in calculating the final cost of exchanged energy. Due to the significant cost of transmission losses in total costs, all transmission system operators are interested in discovering the probabilistic nature of transmission losses as a fundamental requirement for finding the fair method for transmission losses allocation. In this paper, transmission losses are simulated on 110 kV cross-border transmission line using an Adaptive Monte Carlo method. The probability density estimation procedure is performed by the non-linear least-squares method, using the Levenberg–Marquardt algorithm. The Gaussian, log-normal, Rayleigh, four-parameter beta, generalized trapezoidal and the sum of uniform and normal distribution are fitted and the quality of the distribution estimates is compared according to the corresponding values of the Kolmogorov-Smirnov statistic. Furthermore, an additional example presents a distribution fitting procedure on the zero-impedance data of the same transmission line.
  5. 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.





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) 

RealForAll logo color

  • 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

  • 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
  • Osijek Mathematical Gazette

Reviewing

  • AMS Mathematical Reviews (since 2011)

 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.

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)
  • Member of the Higher Education Quality Assurance Board at the Department of Mathematics (since 2006)

Teaching

Konzultacije (Office Hours):

  • ponedjeljkom u 14:00 i utorkom u 13:30 u kabinetu 18 na katu
  • konzultacije je moguće organizirati i u drugom terminu, u dogovoru s nastavnikom

Teme završnih i diplomskih radova:

Courses:

  • Vjerojatnost (Probability), Department of Mathematics, University of Osijek (winter semester)
  • Slučajni procesi (Stohastic Processes), Department of Mathematics, University of Osijek (spring semester)
  • Matematičke financije (Mathematical Finance), Department of Mathematics, University of Osijek (spring semester)
  • Stručna praksa (Professional practice), Department of Mathematics, University of Osijek

Courses taught:

  • 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)