A characterization of Brownian motion in a Lipschitz domain by its killing distributions
type: Item
instance of: scholarly article
title: A characterization of Brownian motion in a Lipschitz domain by its killing distributions
zbMATH Open document ID: 0723.60099
DOI: 10.1007/BF01258748
author: Zoran Vondraček
published in: Journal of Theoretical Probability
publication date: 1991-01-01T00:00:00Z
review text: The Blumenthal-Getoor-McKean theorem states that if X and Y are two standard Markov processes with identical hitting distributions for the compact sets, then there is a strictly increasing continuous additive functional A of X such that \(X_ t=Y_{A(t)}\) for all t. This paper presents the following refinement of the B-G-MK theorem in the case when X is a Brownian motion in a bounded Lipschitz domain D in \({\mathbb{R}}^ n\), and Y a normal strong Markov process in D with continuous path up to its lifetime \({\tilde \zeta}\): if \(X_{\zeta -}\) and \(Y_{{\tilde \zeta}-}\) have the same law for every starting point, then the conclusion of the B- G-MK theorem holds. The idea for the proof is to show that hitting distributions for compact sets are the same for both processes, and then apply the B-G-MK theorem.
reviewed by: Jean Bertoin
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4192833
zbMATH Keywords: time-change
zbMATH Keywords: kernel function
zbMATH Keywords: Blumenthal-Getoor-McKean theorem
zbMATH Keywords: Lipschitz domain
zbMATH Keywords: hitting distributions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01258748
OpenAlex ID: W2080376846
description: scientific article; zbMATH DE number 4192833