Full characterization of the fractional Poisson process

Politi, Mauro, Kaizoji, Taisei and Scalas, Enrico (2011) Full characterization of the fractional Poisson process. Europhysics Letters, 96 (2). p. 20004. ISSN 0295-5075

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
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Depositing User: Enrico Scalas
Date Deposited: 07 Oct 2013 18:10
Last Modified: 22 Mar 2017 18:41
URI: http://sro.sussex.ac.uk/id/eprint/46606

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