The space-fractional Poisson process

Enzo Orsingher and Federico Polito

Statistics & Probability Letters, 2012, vol. 82, issue 4, 852-858

Abstract: In this paper, we introduce the space-fractional Poisson process whose state probabilities pkα(t), t≥0, α∈(0,1], are governed by the equations (d/dt)pkα(t)=−λα(1−B)αpkα(t), where (1−B)α is the fractional difference operator found in the time series analysis. We explicitly obtain the distributions pkα(t), the probability generating functions Gα(u,t), which are also expressed as distributions of the minimum of i.i.d. uniform random variables. The comparison with the time-fractional Poisson process is investigated and finally, we arrive at the more general space–time-fractional Poisson process of which we give the explicit distribution.

Keywords: Space-fractional Poisson process; Backward shift operator; Discrete stable distributions; Stable subordinator; Space–time fractional Poisson process (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (19)

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DOI: 10.1016/j.spl.2011.12.018

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