Multivariate fractional Poisson processes and compound sums

TL;DR

This paper introduces multivariate space-time fractional Poisson processes using common random time-changes of independent classical Poisson processes, extending univariate equations with fractional derivatives and difference operators.

Contribution

It presents a novel framework for multivariate fractional Poisson processes and derives new fractional differential equations governing their behavior.

Findings

Derived equations using fractional derivatives and difference operators

Extended univariate fractional Poisson process equations to multivariate cases

Included analysis of compound processes within the multivariate fractional framework

Abstract

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.