Lévy processes with values in locally convex Suslin spaces

2015/10/02 by Florian Baumgartner, Baumgartner, Florian
Economics, Econometrics and Finance · Mathematics · #28C20 (Secondary) #60B11 (Primary) #60G17 #60G51 #Advanced Banach Space Theory #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1510.00538

openalex publication_date 2015/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a Lévy-Itô decomposition of sample paths of Lévy processes with values in complete locally convex Suslin spaces. This class of state spaces contains the well investigated examples of separable Banach spaces, as well as Fréchet or distribution spaces among many others. Sufficient conditions for the existence of a pathwise compensated Poisson integral handling infinite activity of the Lévy process are given.

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