In this article, we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities. Furthermore, we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.
Heng ZUO
,
Zhaohui SHEN
,
Guanglin RANG
. HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS[J]. Acta mathematica scientia, Series B, 2021
, 41(1)
: 67
-84
.
DOI: 10.1007/s10473-021-0104-6
[1] Applebaum D. Lévy Processes and Stochastic Calculus. Cambridge:Cambridge University Press, 2009
[2] Barndorff-Nielsen O E, Pedersen J, Sato K. Multivariate subordination, self-decomposability and stability. Advances in Applied Probability, 2001, 33(1):160-187
[3] Bochner S. Diffffusion equation and stochastic processes. PNAS, USA, 1949, 35(7):368-370
[4] Buchmann B, Kaehler B, Maller R. Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing. Stochastic Processes and their Applications, 2017, 127(7):2208-2242
[5] Cont R, Tankov P. Financial Modelling with Jump Processes. London:Chapman & Hall, 2003
[6] Dickson D C M, Hughes B D, Zhang L Z. The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims. Scandinavian Actuarial Journal, 2005, 2005(5):358-376
[7] Kostadinova K L, Minkova L D. On the Poisson process of order k. Pliska Studia Mathematica Bulgarica, 2013, 22(1):117-128
[8] Laskin,N. Fractional Poisson process. Commun Nonlinear Sci Numer Simul, 2003, 8(3/4):201-213
[9] Laskin N. Some applications of the fractional Poisson probability distribution. J Math Phy, 2008, 50(11):201-227
[10] Liu Y, Yang W Q, Hu Y J. On the ruin functions for a correlated aggregate claims model with Poisson and Erlang risk processes. Acta Math Sci, 2006, 26B(2):321-330
[11] Orsingher E, Polito F. The space-fractional Poisson process. Stat Prob Lett, 2012, 82(4):852-858
[12] Philippou A N. The Poisson and compound Poisson distribution of order k and some of their properties. Zapiski Nauchnykh Seminarov POMI, 1983, 130:175-180
[13] Philippou A N, Georghiou C, Philippou G N. A generalized geometric distribution and some of its properties. Stat Prob Lett, 1983, 1(4):171-175
[14] Sato K. Levy Processes and Infinitely Divisible Distributions. Cambridge:Cambridge University Press, 1999
[15] Sengar A S, Maheshwari A, Upadhye N S. Time-changed Poisson processes of order k. Stoch Anal Appl, 2020, 38(1):124-148
[16] Sengar A S, Maheshwari A, Orsingher E. Superposition of time-changed Poisson processes and their hitting times. 2019, arXiv preprint. https://arxiv.org/abs/1909.13213v1
