The space-fractional Poisson process
By Enzo Orsingher, Federico Polito. 2011
116 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Modeling and Simulation, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/df2f5c8c3f079cb210a85329b8ea8e2bfce48061
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In Applied Mathematics
- Federico Polito
- Enzo Orsingher
- Roberto Garra
- A. Di Crescenzo
- Barbara Martinucci
- Alessandra Meoli
- Sergei Rogosin
- Luisa Beghin
In Modeling and Simulation
- Federico Polito
- Roberto Garra
- Enzo Orsingher
- A. Di Crescenzo
- Barbara Martinucci
- Alessandra Meoli
- Sergei Rogosin
- Luisa Beghin
In Statistics and Probability
Citations in the corpus
- A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability (2017, background): “onal equations with varying coefficients. Theorem 1. For n 2(0,1), the function g(u,t) = un n1 E ;1,n(lut) En;1,n(lt) = un 1G(u,t), satisfies the equation u d du n g(u,t) = ltug(u,t)+ un 1 Gn(n 1) , (26) where u d du n is the Caputo-Hadamard fractional derivative of order n. Proof. By direct calcula”
- A fractional counting process and its connection with the Poisson process (2015, background): “…the possibility of jumps of amplitude larger than 1 have been obtained recently through the interesting space-fractional Poisson process (cf. Orsingher and Polito (2012)) and, more generally, through the class of point processes studied in Orsingher and Toaldo (2015) and Polito and Scalas…”