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Limit theorems for the fractional non-homogeneous Poisson process

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posted on 2023-06-09, 16:41 authored by Nikolai Leonenko, Enrico Scalas, Mailan Trinh
The fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverse a-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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Applied Probability

ISSN

0021-9002

Publisher

Cambridge University Press

Issue

1

Volume

56

Page range

246-264

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-01-31

First Open Access (FOA) Date

2019-04-11

First Compliant Deposit (FCD) Date

2019-01-30

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