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Limit theorems for the fractional non-homogeneous Poisson process

Leonenko, Nikolai, Scalas, Enrico and Trinh, Mailan 2019. Limit theorems for the fractional non-homogeneous Poisson process. Journal of Applied Probability 56 (1) , pp. 246-264. 10.1017/jpr.2019.16

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Abstract

The fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverse α-stable subordinator. We propose a similar definition for the (nonhomogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional nonhomogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe’s theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Applied Probability Trust
ISSN: 0021-9002
Date of First Compliant Deposit: 29 January 2019
Date of Acceptance: 29 January 2019
Last Modified: 18 Oct 2019 05:54
URI: http://orca.cf.ac.uk/id/eprint/119019

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