Lévy flows on manifolds and Lévy processes on Lie groups
type: Item
instance of: scholarly article
title: Lévy flows on manifolds and Lévy processes on Lie groups
zbMATH Open document ID: 0804.58057
author: David Applebaum
author: Hiroshi Kunita
published in: Journal of Mathematics of Kyoto University
publication date: 1994-06-08T00:00:00Z
review text: For an arbitrary (not necessarily compact) manifold \(M\) the authors consider the problem of constructing the stochastic flow of diffeomorphisms of \(M\) corresponding to a stochastic differential equation (SDE) driven by a Lévy process. The Lévy process driving the SDE is supposed to have finitely many degrees of freedom, so that the Poisson random measure component of the process is itself defined on a finite dimensional manifold \(N\). The authors construct the flow in two particular cases: (i) \(N\) is a Euclidean space, and the Lie algebra generated by the vector fields driving the SDE is finitely dimensional, and (ii) \(N\) is a finite dimensional Lie group, and the vector fields driving the SDE are left invariant.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 584585
zbMATH Keywords: stochastic flow
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: Lévy process
Wikidata QID: Q115240417
reviewed by: Vadim A. Kaimanovich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519132
OpenAlex ID: W2224043109
DOI: 10.1215/KJM/1250519132
description: scientific article; zbMATH DE number 584585