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Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse
, Vellaisamy P
Published in Springer
Volume: 32
Issue: 3
Pages: 1278 - 1305

In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Lévy subordinator and the inverse of the Lévy 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. The bivariate distributions of the TCFPP-II are derived. Some specific examples for both the processes are discussed. Finally, we present simulations of the sample paths of these processes.

About the journal
JournalData powered by TypesetJournal of Theoretical Probability
PublisherData powered by TypesetSpringer
Open AccessNo