Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator
Probability
2016-08-09 v1
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.
Keywords
Cite
@article{arxiv.1608.02224,
title = {Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator},
author = {Luisa Beghin and Costantino Ricciuti},
journal= {arXiv preprint arXiv:1608.02224},
year = {2016}
}