Autore:
E. Orsingher, F. Polito
Abstract:
In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where $(1-B)^\alpha$ is the fractional difference operator found in the study of time series analysis. We explicitly obtain the distributions $p_k^\alpha(t)$, the probability generating functions $G_\alpha(u,t)$, 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.
Parole Chiave:
Space-fractional Poisson process, Backward shift operator, Discrete stable distributions, Stable subordinator, Space-time fractional Poisson process.
Tipo di pubblicazione:
Rapporto Tecnico
Codice Pubblicazione:
13
Allegato Pubblicazione:
Contatto:
ISSN:
2279-798X