Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator

Luisa Beghin; Costantino Ricciuti

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arXiv · 1608.02224

Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator

Luisa Beghin·Costantino Ricciuti

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Abstract

The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its inverse, respectively. The aim of this paper is to study non-homogeneous versions of such models, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. Firstly, we consider the Poisson process time-changed by H and we obtain its explicit distribution and governing equation. Then, by using the right-continuous inverse of H, we define an inhomogeneous analogue of the time-fractional Poisson process.

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Luisa Beghin, Costantino Ricciuti. 2016-08-07. Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator. https://arxiv.org/abs/1608.02224

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