Results 1 to 10 of about 50,463 (273)
On the Fractional Poisson Process and the Discretized Stable Subordinator [PDF]
Axioms, 2015 We consider the renewal counting number process N = N(t) as a forward march over the non-negative integers with independent identically distributed waiting times.
Rudolf Gorenflo, Francesco Mainardi
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Saigo Space-Time Fractional Poisson Process via Adomian Decomposition Method [PDF]
Statistics & Probability Letters, 2017 We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM).
Kataria, K. K., Vellaisamy, P.
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Some Compound Fractional Poisson Processes
Fractal and Fractional, 2022 In this paper, we introduce and study fractional versions of the Bell–Touchard process, the Poisson-logarithmic process and the generalized Pólya–Aeppli process.
Mostafizar Khandakar +1 more
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Alternative Forms of Compound Fractional Poisson Processes [PDF]
Abstract and Applied Analysis, 2012 We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves.
Luisa Beghin, Claudio Macci
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On the Integral of Fractional Poisson Processes [PDF]
Statistics & Probability Letters, 2013 In this paper we consider the Riemann--Liouville fractional integral $\mathcal{N}^{\alpha,\nu}(t)= \frac{1}{\Gamma(\alpha)} \int_0^t (t-s)^{\alpha-1}N^\nu(s) \, \mathrm ds $, where $N^\nu(t)$, $t \ge 0$, is a fractional Poisson process of order $\nu \in (
Orsingher, Enzo, Polito, Federico
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A class of CTRWs: Compound fractional Poisson processes [PDF]
, 2011 This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known L\'evy process: The compound Poisson process.
Scalas, Enrico
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Large deviations for fractional Poisson processes [PDF]
Statistics & Probability Letters, 2012 We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance model with ...
Beghin, Luisa, Macci, Claudio
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Fractional processes: from Poisson to branching one [PDF]
International Journal of Bifurcation and Chaos, 2010 Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for construction of the ...
D. O. CAHOY +6 more
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Studies on generalized Yule models
Modern Stochastics: Theory and Applications, 2018 We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes
Federico Polito
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Fractional Poisson process with random drift
Electronic Journal of Probability, 2014 We study the connection between PDEs and L\'{e}vy processes running with clocks given by time-changed Poisson processes with stochastic drifts. The random times we deal with are therefore given by time-changed Poissonian jumps related to some Frobenious ...
Beghin, Luisa, D'Ovidio, Mirko
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