Radiophysics and Quantum Electronics

, Volume 43, Issue 9, pp 738-741

First online:

Fractional Poisson Law

  • O. N. RepinAffiliated withN. I. Lobachevsky State University
  • , A. I. SaichevAffiliated withN. I. Lobachevsky State University

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We consider a Poisson process with random intensity for which the distribution of intervals between jumps is described by an equation with fractional derivatives. The distribution of random intensity of this process and the generating function of the jump number are obtained in explicit form. It is noted that the studied fractional Poisson law can be used for statistical description of chaotic processes of different physical nature demonstrating the phenomenon of anomalous diffusion.