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A generalization of the space-fractional Poisson process and its connection to some Lévy processes

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posted on 2023-06-09, 00:34 authored by Federico Polito, Enrico Scalas
The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related to a specific subordinator for which it is possible to explicitly write the characterizing Lévy measure. Connections are highlighted to Prabhakar derivatives, specific convolution-type integral operators. Finally, we study the effect of introducing Prabhakar derivatives also in time.

History

Publication status

  • Published

File Version

  • Published version

Journal

Electronic Communications in Probability

ISSN

1083-589X

Publisher

Institute of Mathematical Statistics

Volume

21

Page range

20-34

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-03-15

First Open Access (FOA) Date

2016-03-15

First Compliant Deposit (FCD) Date

2016-03-14

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