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Full characterization of the fractional Poisson process

journal contribution
posted on 2023-06-08, 16:01 authored by Mauro Politi, Taisei Kaizoji, Enrico Scalas
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poisson process, the fractional Poisson process does not have stationary and independent increments. It is not a L\'evy process and it is not a Markov process. In this letter, we present formulae for its finite-dimensional distribution functions, fully characterizing the process. These exact analytical results are compared to Monte Carlo simulations.

History

Publication status

  • Published

Journal

Europhysics Letters

ISSN

0295-5075

Publisher

EDP Sciences

Issue

2

Volume

96

Page range

20004

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-10-07

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