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Full characterization of the fractional Poisson process

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  • Mauro Politi
  • Taisei Kaizoji
  • 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.

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File URL: http://arxiv.org/pdf/1104.4234
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1104.4234.

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Date of creation: Apr 2011
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Handle: RePEc:arx:papers:1104.4234

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Web page: http://arxiv.org/

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Cited by:
  1. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
  2. Orsingher, Enzo & Polito, Federico, 2013. "On the integral of fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1006-1017.
  3. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.

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