Some Time-changed fractional Poisson processes
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.
Keywords
Cite
@article{arxiv.1703.03547,
title = {Some Time-changed fractional Poisson processes},
author = {A. Maheshwari and P. Vellaisamy},
journal= {arXiv preprint arXiv:1703.03547},
year = {2017}
}
Comments
25 pages, 07 figures