| Issue |
EPL
Volume 96, Number 2, October 2011
|
|
|---|---|---|
| Article Number | 20004 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/96/20004 | |
| Published online | 29 September 2011 | |
Full characterization of the fractional Poisson process
1
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
Received:
1
June
2011
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.