A fractional counting process and its connection with the Poisson process

zbMath1337.60063arXiv1503.06486MaRDI QIDQ2805288

Barbara Martinucci, Alessandra Meoli, Antonio Di Crescenzo

Publication date: 11 May 2016

Full work available at URL: https://arxiv.org/abs/1503.06486

zbMATH Keywords

Mittag-Leffler functionfirst passage timeWright functionrandom timefractional difference-differential equationsfractional Poisson processfractional counting process

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stopping times; optimal stopping problems; gambling theory (60G40) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Fractional ordinary differential equations (34A08)

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Extended eigenvalue-eigenvector method ⋮ Convoluted Fractional Poisson Process ⋮ Competing risks driven by Mittag-Leffler distributions, under copula and time transformed exponential model ⋮ Fractional immigration-death processes ⋮ On the convolution of Mittag–Leffler distributions and its applications to fractional point processes ⋮ Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator ⋮ On a jump-telegraph process driven by an alternating fractional Poisson process ⋮ Probabilistic analysis of systems alternating for state-dependent dichotomous noise ⋮ Limit theorems for the fractional nonhomogeneous Poisson process ⋮ The fractional birth process with power-law immigration ⋮ On a fractional alternating Poisson process ⋮ Generalized fractional counting process ⋮ Skellam and time-changed variants of the generalized fractional counting process ⋮ On the sum of independent generalized Mittag–Leffler random variables and the related fractional processes

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