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Time-changed Poisson processes of order k
Published in Taylor and Francis Inc.
Volume: 38
Issue: 1
Pages: 124 - 148
In this article, we study the Poisson process of order (Formula presented.) (PPoK) time-changed with an independent L'evy 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.
About the journal
JournalData powered by TypesetStochastic Analysis and Applications
PublisherData powered by TypesetTaylor and Francis Inc.
Open AccessYes