Compound Poisson processes and Lévy processes in groups and symmetric spaces
type: Item
instance of: scholarly article
title: Compound Poisson processes and Lévy processes in groups and symmetric spaces
zbMATH Open document ID: 0985.60047
DOI: 10.1023/A:1007845508326
author: David Applebaum
published in: Journal of Theoretical Probability
publication date: 2002-05-09T00:00:00Z
review text: The paper deals with three themes. The first is the description of the paths of Lévy processes in groups. The author shows that the paths of a Lévy process in a (locally compact Hausdorff) group can be obtained as the almost sure limit of a sequence of Brownian motions interlaced with random jumps. The second theme is the characterisation of Lévy processes in Riemannian globally symmetric spaces. Results of \textit{R. Gangolli} [Pac. J. Math. 15, 477---496 (1965; Zbl 0141.14903)] are generalised and a simpler proof of Gangolli's Lévy-Khinchin formula is given. Finally, the third theme is constructing Fock space realisations for spherically symmetric Lévy processes in groups and factorizable representations of current groups.
reviewed by: Uwe Franz
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 81S25
zbMATH DE Number: 1512525
zbMATH Keywords: compound Poisson process
zbMATH Keywords: Lévy processes in Lie groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1512525