Odjel za matematiku

Danijel Grahovac

 

AVM6205 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

  1. R. Scitovski, K. Sabo, D. Grahovac, Š. Ungar, Minimal distance index — A new clustering performance metrics, Information Sciences (2023), prihvaćen za objavljivanje
  2. D. Grahovac, N.N. Leonenko, M. Taqqu, Intermittency and Multiscaling in Limit Theorems, Fractals 30/7 (2022), 1-18
  3. D. Grahovac, Intermittency in the small-time behavior of Levy processes, Statistics & Probability Letters 187/109507 (2022), 1-8
  4. 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
  5. 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
  6. D. Grahovac, Multifractal processes: Definition, properties and new examples, Chaos, Solitons & Fractals 134/109735 (2020)
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. D. Grahovac, N.N. Leonenko, Bounds on the support of the multifractal spectrum of stochastic processes, Fractals 26/04 (2018), 1-21
  13. 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
  14. D. Grahovac, N.N. Leonenko, M. Taqqu, Intermittency of trawl processes, Statistics & Probability Letters 137 (2018), 235-242
  15. R. Grbić, D. Grahovac, R. Scitovski, A method for solving the multiple ellipses detection problem, Pattern Recognition 60 (2016), 824-834
  16. 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
  17. 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
  18. D. Grahovac, N. Šuvak, Heavy-tailed modeling of CROBEX, Financial Theory and Practice 39/4 (2015), 411-430
  19. 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
  20. D. Grahovac, N.N. Leonenko, Detecting multifractal stochastic processes under heavy-tailed effects, Chaos, Solitons & Fractals 66 (2014), 78-89


Refereed Proceedings

  1. 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

  1. D. Grahovac, L. Grgić, Dugoročna zavisnost, Osječki matematički list 19/1 (2019), 15-29
  2. D. Grahovac, A. Leko, Modeliranje rizika u osiguranju, Osječki matematički list 15/2 (2015), 113-129
  3. D. Grahovac, Two-dimensional interpolation spline, Osječki matematički list 10/1 (2010), 59-69


Books

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


Softwares

  1. 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.

Professional Activities

Editorial Boards

 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