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2014 Fractional Poisson process with random drift
Luisa Beghin, Mirko D'Ovidio
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Electron. J. Probab. 19: 1-26 (2014). DOI: 10.1214/EJP.v19-3258


We study the connection between PDEs and Lévy 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 Frobenius-Perron operators $K$ associated to random translations. Moreover, we also consider their hitting times as a random clock. Thus, we study processes driven by equations involving time-fractional operators (modelling memory) and fractional powers of the difference operator $I-K$ (modelling jumps). For this large class of processes we also provide, in some cases, the explicit representation of the transition probability laws. To this aim, we show that a special role is played by the translation operator associated to the representation of the Poisson semigroup.


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Luisa Beghin. Mirko D'Ovidio. "Fractional Poisson process with random drift." Electron. J. Probab. 19 1 - 26, 2014.


Accepted: 30 December 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1334.60053
MathSciNet: MR3304182
Digital Object Identifier: 10.1214/EJP.v19-3258

Primary: 60G35
Secondary: 60G50

Keywords: fractional equation , Poisson process , Poisson semigroup , random drift , time-change


Vol.19 • 2014
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