Danijel Grahovac

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:	dgrahova @ mathos.hr
Google Scholar profil
office:	18 (first floor)

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

Journal Publications

R. Scitovski, K. Sabo, D. Grahovac, Š. Ungar, Minimal distance index — A new clustering performance metrics, Information Sciences 640/119046 (2023)
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

Refereed Proceedings

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

Others

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

Books

R. Scitovski, K. Sabo, D. Grahovac, Globalna optimizacija, Sveučilište Josipa Jurja Strossmayera u Osijeku, Odjel za matematiku, Osijek, 2017.

Softwares

R. Scitovski, K. Sabo, D. Grahovac, Globalna optimizacija (2017)

Projects

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.