Time-changed Poisson processes of order k

2018/11/12 by Ayushi S. Sengar, Aditya Maheshwari, Sengar, Ayushi S. +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G51 #60G55 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.1811.04567

openalex publication_date 2018/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the Poisson process of order k (PPoK) time-changed with an independent Lévy subordinator and its inverse, which we call respectively, as TCPPoK-I and TCPPoK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCPPoK-I. Further, we study the governing difference-differential equations of the TCPPoK-I for the case inverse Gaussian subordinator. Similarly, we study the distributional properties, asymptotic moments and the governing difference-differential equation of TCPPoK-II. As an application to ruin theory, we give a governing differential equation of ruin probability in insurance ruin using these processes. Finally, we present some simulated sample paths of both the processes.

Citations

• The Space-Fractional Poisson Process
• Counting processes with Bernštein intertimes and random jumps
• On the long-range dependence of fractional Poisson and negative binomial processes
• Inverse tempered stable subordinators

Cited by

• Time-changed generalized fractional Skellam process

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