Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse

A. Maheshwari () and P. Vellaisamy ()
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A. Maheshwari: Indian Institute of Management Indore
P. Vellaisamy: Indian Institute of Technology Bombay

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1278-1305

Abstract: Abstract 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.

Keywords: Lévy subordinator; Fractional Poisson process; Simulation; 60G22; 60G55 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10959-017-0797-6

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