LITERATURA:

Kallenberg, O. (2017). Random measures, theory and applications

Last, G., & Penrose, M. (2017). Lectures on the Poisson process

Resnick, S. I. (2008). Extreme values, regular variation, and point processes 

Resnick, S. I. (2007). Heavy-tail phenomena: probabilistic and statistical modeling

Chiu, S. N., Stoyan, D., Kendall, W. S., & Mecke, J. (2013). Stochastic geometry and its applications

Baddeley, A. (2008). Analysing spatial point patterns in R

TERMIN  PREDAVANJA: srijeda 14-16 sati (105)

TEME ZA SEMINAR (PRIJEDLOZI)

1) Veza Poissonovih tockovnih procesa i Levyjevih procesa. Osnovna literatura: Kallenberg, O. (2021). Foundations of modern probability (Vol. 2). 3rd ed. Chapter 16. (Poglavlje 16, posebno teoremi 16.3 i 16.12). 

2) Poisson Dirichletovi procesi. Osnovna literatura: Klenke, A. (2013). Probability theory: a comprehensive course. Springer (posebno Odj 24.3), Billingsley, P. (2013). Convergence of probability measures. Wiley & Sons.

3) Pitman-Yor procesi. Osnovna literatura: Pitman, J. (2006). Combinatorial stochastic processes: Ecole d'eté de probabilités de saint-flour xxxii-2002. Springer, Perman, M., Pitman, J., & Yor, M. (1992). Size-biased sampling of Poisson point processes and excursions. Probability Theory and Related Fields, 92(1), 21-39

4) Konvergencija prema Poissonovim procesima i Steinova metoda.  Bobrowski, O., Schulte, M., & Yogeshwaran, D. (2021). Poisson process approximation under stabilization and Palm coupling. arXiv preprint arXiv:2104.13261. Ann. H. Lebesgue 5 (2022), 1489–1534

5) Konvergencija prema slozenim Poissonovim procesima. Grigelionisov teorem.  Basrak, B., & Planinić, H. (2021). Compound Poisson approximation for regularly varying fields with application to sequence alignment. Bernoulli