HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

doi:10.1007/s10473-021-0104-6

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (1): 67-84.doi: 10.1007/s10473-021-0104-6

• Articles • Previous Articles Next Articles

HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

Heng ZUO¹, Zhaohui SHEN¹, Guanglin RANG^1,2

1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China;
2. Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China

Received:2019-12-18 Revised:2020-09-11 Online:2021-02-25 Published:2021-04-06
Contact: Heng ZUO E-mail:zuoheng@whu.edu.cn
About author:Zhaohui SHEN,E-mail: shenzh@whu.edu.cn;Guanglin RANG,E-mail:glrang.math@whu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (11571262, 11731012 and 11971361).

Abstract

CLC Number:

60E10

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.

Trendmd

References

[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

HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 13

Metrics

Comments

Recommended 0

[1]	Jacek DZIOK. HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS [J]. Acta mathematica scientia,Series B, 2019, 39(6): 1661-1673.
[2]	Muhammed ARIF, Shahid MAHMOOD, Janusz SOKÓŁ, Jacek DZIOK. NEW SUBCLASS OF ANALYTIC FUNCTIONS IN CONICAL DOMAIN ASSOCIATED WITH A LINEAR OPERATOR [J]. Acta mathematica scientia,Series B, 2016, 36(3): 704-716.
[3]	TANG Huo, Erhan DENIZ. THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS [J]. Acta mathematica scientia,Series B, 2014, 34(6): 1707-1719.
[4]	Mohamed K. AOUF, Teodor BULBOACA, Tamer M. SEOUDY. CERTAIN FAMILY OF INTEGRAL OPERATORS PRESERVING SUBORDINATION AND SUPERORDINATION [J]. Acta mathematica scientia,Series B, 2014, 34(4): 1166-1178.
[5]	Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH. SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR [J]. Acta mathematica scientia,Series B, 2014, 34(2): 367-379.
[6]	PENG Zhi-Gang, HAN Qiu-Qiu. ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS [J]. Acta mathematica scientia,Series B, 2014, 34(1): 228-240.
[7]	Jacek DZIOK\|Ravinder Krishna RAINA\|Janusz SOKóL. DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS [J]. Acta mathematica scientia,Series B, 2013, 33(3): 609-620.
[8]	S. HUSSAIN, J. SOKóL. ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1399-1407.
[9]	Nak Eun Cho. SANDWICH-TYPE THEOREMS FOR MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH THE LIU-SRIVASTAVA OPERATOR [J]. Acta mathematica scientia,Series B, 2012, 32(3): 929-941.
[10]	Teodor Bulboaca. SANDWICH-TYPE RESULTS FOR A CLASS OF CONVEX INTEGRAL OPERATORS [J]. Acta mathematica scientia,Series B, 2012, 32(3): 989-1001.
[11]	J. Dziok. CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS [J]. Acta mathematica scientia,Series B, 2012, 32(2): 765-774.
[12]	J. Dziok . A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS [J]. Acta mathematica scientia,Series B, 2011, 31(4): 1357-1366.
[13]	LIU Ming-Sheng. ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION [J]. Acta mathematica scientia,Series B, 2002, 22(3): 388-392.