A class of path-valued Markov processes and its applications to superprocesses
type: Item
instance of: scholarly article
title: A class of path-valued Markov processes and its applications to superprocesses
zbMATH Open document ID: 0794.60076
DOI: 10.1007/BF01197336
publication date: 1994-08-28T00:00:00Z
review text: Let \((\xi_ s)\) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with \((\xi_ s)\), which is closely related to the so-called superprocess with spatial motion \((\xi_ s)\). In particular, a subset \(H\) of the state space of \((\xi_ s)\) intersects the range of the superprocess if and only if the set of paths that hit \(H\) is not polar for the path-valued process. The latter property can be investigated by using the tools of the potential theory of symmetric Markov processes: A set is not polar if and only if it supports a measure of finite energy. The same approach can be applied to study sets that are polar for the graph of the superprocess. In the special case when \((\xi_ s)\) is a diffusion process, we recover certain results recently obtained by Dynkin.
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 569037
zbMATH Keywords: continuous Markov process
zbMATH Keywords: superprocess
zbMATH Keywords: potential theory
zbMATH Keywords: graph of the superprocess
zbMATH Keywords: diffusion process
author: J.-F. Le Gall
reviewed by: J.-F. Le Gall
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569037