Full characterization of the fractional Poisson process
SSRI & Department of Economics and Business, International Christian University - 3-10-2 Osawa, Mitaka, Tokyo, 181-8585 Japan
2 Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “Amedeo Avogadro” Viale T. Michel 11, I-15121 Alessandria, Italy, EU
3 Basque Center for Applied Mathematics - Bizkaia Technology Park, Building 500, E-48160, Derio, Spain, EU
Accepted: 27 August 2011
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 Lévy 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.
PACS: 02.50.Ey – Stochastic processes / 05.10.Ln – Monte Carlo methods
© EPLA, 2011