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Full characterization of the fractional Poisson process

By Mauro Politi, Taisei Kaizoji and Enrico Scalas

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.Comment: 4 figures, paper submitted to PR

Topics: Mathematics - Probability, Physics - Data Analysis, Statistics and Probability, Quantitative Finance - Statistical Finance, 60G55, 60G50, 60G22
Year: 2011
DOI identifier: 10.1209/0295-5075/96/20004
OAI identifier: oai:arXiv.org:1104.4234
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