On the properites of Poisson random measures associated with a G-Levy process

TL;DR

This paper investigates the properties of Poisson random measures linked to G-Levy processes, establishing conditions for integrals to belong to good spaces and decomposing G-Levy processes into continuous and jump components.

Contribution

It introduces new conditions for Poisson integrals to be in good spaces and provides a pathwise decomposition of G-Levy processes into generalized G-Brownian motion and pure-jump processes.

Findings

Poisson integral is a G-Levy process under certain conditions

Pathwise decomposition of G-Levy process into two components

Conditions for integrand quasi-continuity and integral quasi-continuity

Abstract

In this paper we study the properties of the Poisson random measure and the Poisson integral associated with a G-Levy process. We prove that a Poisson integral is a G-Levy process and give the conditions which ensure that a Poisson integral belongs to a good space of random variables. In particular, we study the relation between the quasi- continuity of an integrand and the quasi-continuity of the integral. Lastly, we apply the results to establish the pathwise decomposition of a G-Levy process into a generalized G-Brownian motion and a pure-jump G-Levy process and prove that both processes belong to a good space of random variables.