Some Time-changed fractional Poisson processes

A. Maheshwari; P. Vellaisamy

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arXiv · 1703.03547

Some Time-changed fractional Poisson processes

A. Maheshwari·P. Vellaisamy

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Abstract

In this paper, we study the fractional Poisson process (FPP) time-changed by an independent L\'evy subordinator and the inverse of the L\'evy subordinator, which we call TCFPP-I and TCFPP-II, respectively. Various distributional properties of these processes are established. We show that, under certain conditions, the TCFPP-I has the long-range dependence property and also its law of iterated logarithm is proved. It is shown that the TCFPP-II is a renewal process and its waiting time distribution is identified. Its bivariate distributions and also the governing difference-differential equation are derived. Some specific examples for both the processes are discussed. Finally, we present the simulations of the sample paths of these processes.

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BibTeX RIS

A. Maheshwari, P. Vellaisamy. 2017-03-10. Some Time-changed fractional Poisson processes. https://arxiv.org/abs/1703.03547

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