Danijel Grahovac
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Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR-31000, Croatia
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Research Interests
- Limit theorems, scaling properties of stochastic processes (self-similarity, multifractal processes), heavy-tailed distributions
Degrees
- PhD in mathematics, Faculty of Natural Science, Department of Mathematics, University of Zagreb, 2015
- Thesis: Scaling properties of stochastic processes with applications to parameter estimation and sample path properties, supervisors: N. N. Leonenko, M. Benšić
- MSc in Mathematics, Financial and Business Mathematics, Department of Mathematics, University of Osijek, Croatia, 2010
- MSc in Mathematics and Computer Science Education, Department of Mathematics, University of Osijek, Croatia, 2016
- BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2008
Publications
- R. Scitovski, K. Sabo, D. Grahovac, Š. Ungar, Minimal distance index — A new clustering performance metrics, Information Sciences (2023), prihvaćen za objavljivanje
- D. Grahovac, N.N. Leonenko, M. Taqqu, Intermittency and Multiscaling in Limit Theorems, Fractals 30/7 (2022), 1-18
- D. Grahovac, Intermittency in the small-time behavior of Levy processes, Statistics & Probability Letters 187/109507 (2022), 1-8
- D. Grahovac, N.N. Leonenko, M. Taqqu, Intermittency and infinite variance: the case of integrated supOU processes, Electronic Journal of Probability 26 (2021), 1-31
- K. Sabo, D. Grahovac, R. Scitovski, Incremental method for multiple line detection problem - iterative reweighted approach, Mathematics and Computers in Simulation 178 (2020), 588-602
- D. Grahovac, Multifractal processes: Definition, properties and new examples, Chaos, Solitons & Fractals 134/109735 (2020)
- D. Grahovac, N.N. Leonenko, M. Taqqu, The multifaceted behavior of integrated supOU processes: The infinite variance case, Journal of Theoretical Probability 33 (2020), 1801-1831
- F. Avram, D. Grahovac, C. Vardar-Acar, The W,Z scale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems, ESAIM: Probability and Statistics 24 (2020), 454-525
- D. Grahovac, N.N. Leonenko, M. Taqqu, Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes, Stochastic Processes and their Applications 129/12 (2019), 5113-5150
- D. Grahovac, N.N. Leonenko, A. Sikorskii, M. Taqqu, The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes, Bernoulli 25/3 (2019), 2029-2050
- F. Avram, D. Grahovac, C. Vardar-Acar, The W,Z/ν,δ Paradigm for the First Passage of Strong Markov Processes without Positive Jumps, Risks 7/1-18 (2019), 1-15
- D. Grahovac, N.N. Leonenko, Bounds on the support of the multifractal spectrum of stochastic processes, Fractals 26/04 (2018), 1-21
- D. Grahovac, Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims, Methodology and Computing in Applied Probability 20/1 (2018), 273-288
- D. Grahovac, N.N. Leonenko, M. Taqqu, Intermittency of trawl processes, Statistics & Probability Letters 137 (2018), 235-242
- R. Grbić, D. Grahovac, R. Scitovski, A method for solving the multiple ellipses detection problem, Pattern Recognition 60 (2016), 824-834
- D. Grahovac, N.N. Leonenko, A. Sikorskii, I. Tešnjak, Intermittency of superpositions of Ornstein-Uhlenbeck type processes, Journal of Statistical Physics 165/2 (2016), 390-408
- D. Grahovac, M. Jia, N.N. Leonenko, E. Taufer, Asymptotic properties of the partition function and applications in tail index inference of heavy-tailed data, Statistics - a Journal of Theoretical and Applied Statistics 49/6 (2015), 1221-1242
- D. Grahovac, N. Šuvak, Heavy-tailed modeling of CROBEX, Financial Theory and Practice 39/4 (2015), 411-430
- D. Grahovac, N.N. Leonenko, M. Taqqu, Scaling properties of the empirical structure function of linear fractional stable motion and estimation of its parameters, Journal of Statistical Physics 158/1 (2015), 105-119
- D. Grahovac, N.N. Leonenko, Detecting multifractal stochastic processes under heavy-tailed effects, Chaos, Solitons & Fractals 66 (2014), 78-89
- D. Grahovac, M. Jia, N.N. Leonenko, E. Taufer, On the tail index inference based on the scaling function method, 18th European Young Statisticians Meeting, Osijek, Croatia, 2013, 39-45
- D. Grahovac, L. Grgić, Dugoročna zavisnost, Osječki matematički list 19/1 (2019), 15-29
- D. Grahovac, A. Leko, Modeliranje rizika u osiguranju, Osječki matematički list 15/2 (2015), 113-129
- D. Grahovac, Two-dimensional interpolation spline, Osječki matematički list 10/1 (2010), 59-69
- R. Scitovski, K. Sabo, D. Grahovac, Globalna optimizacija, Sveučilište Josipa Jurja Strossmayera u Osijeku, Odjel za matematiku, Osijek, 2017.
- R. Scitovski, K. Sabo, D. Grahovac, Globalna optimizacija (2017)
Projects
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Limiting behavior of intermittent processes and diffusions
Project runs in academic year 2019/2020. Project leader: Danijel Grahovac. Project funded by University of Osijek. -
Stochastic models with long-range dependence
Project runs in academic year 2017/2018. Project leader: Nenad Šuvak. Project funded by University of Osijek. -
Fractional Pearson Diffusions
Project run in academic year 2014/2015. Project leader: Nenad Šuvak. Project funded by University of Osijek. -
Development and Application of Growth Potential Prediction Models for Small and Medium Enterprises in Croatia
Project runs since June 2014. Project leader: Nataša Šarlija. Project funded by Croatian Science Foundation. -
Statistical aspects of estimation problem in nonlinear parametric models
Project run in 2007-2013. Project leader: Mirta Benšić. Project funded by Croatian Ministry of Science, Education and Sports.
Professional Activities
Editorial Boards- Co-Editor of Croatian Operational Research Review
Committee Memberships
- Member of the Local Organizing Comitee of the 18th European Young Statisticians Meeting, 26-30 August 2013, Osijek, Croatia
Service Activities
- Secretary of the Mathematical Colloquium in Osijek, 2013 - 2017
- Moderator of Optimization and applications seminar 2017 -
Teaching
Konzultacije (Office Hours): srijeda 11:45, u vrijeme ispitnih rokova po dogovoru
Teme diplomskih radova 2022/2023 (pdf)
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Past courses: Databases, Statistics, Stochastic Processes, Numerical Mathematics, Mathematics (Faculty of Economics)
Personal