2014/11/17 by Krzysztof Paczka, Paczka, Krzysztof
Economics, Econometrics and Finance · Mathematics · #60G51 #60H05 #60H10 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #msc:60G51 #msc:60H05 #msc:60H10
paper · pdf · doi:10.48550/arxiv.1411.4660
arxiv created 2014/11/17 · openalex publication_date 2014/11/17 · arxiv updated 2014/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.