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On the fractional Poisson process and the discretized stable subordinator

Probability 2016-01-14 v2 Mathematical Physics math.MP

Abstract

The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed these two processes, concretely the corresponding counting number and Erlang processes, the latter being the processes inverse to the former. Furthermore we have obtained the diffusion limits of all these processes by well-scaled refinement of waiting times and jumps

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Cite

@article{arxiv.1305.3074,
  title  = {On the fractional Poisson process and the discretized stable subordinator},
  author = {Rudolf Gorenflo and Francesco Mainardi},
  journal= {arXiv preprint arXiv:1305.3074},
  year   = {2016}
}

Comments

30 pages, 4 figures. A preliminary version of this paper was an invited talk given by R. Gorenflo at the Conference ICMS2011, held at the International Centre of Mathematical Sciences, Pala-Kerala (India) 3-5 January 2011, devoted to Prof Mathai on the occasion of his 75 birthday