Markov snakes and superprocesses
type: Item
instance of: scholarly article
title: Markov snakes and superprocesses
zbMATH Open document ID: 0862.60072
DOI: 10.1007/BF01246334
author: E. B. Dynkin
author: S. E. Kuznetsov
publication date: 1997-05-25T00:00:00Z
review text: \textit{J.-F. Le Gall} introduced a class of path-valued Markov processes [ibid. 95, No. 1, 25-46 (1993; Zbl 0794.60076)] and obtained a representation of superdiffusions in terms of them. He used these to investigate path properties of superdiffusions and to give a probabilistic approach to the study of a class of nonlinear partial differential equations. The authors present an isomorphism theorem which establishes a one-to-one relation between a class of these path processes, which they call Markov snakes, and a class of superprocesses. This provides two different sets of tools which can be used to study these which are complementary. They also establish the weak convergence of a class of discrete Markov snakes, called simple snakes, which arise from a simple random walk on \(\beta Z_+\) with reflection at zero as \(\beta\to0\). They also consider the class of simple L-snakes (corresponding to the random walk killed on the first return to 0). The corresponding Brownian L-snake is used to describe the limit distributions for additive functionals of the simple L-snake.
reviewed by: Donald A. Dawson
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 822727
zbMATH Keywords: superdiffusions
zbMATH Keywords: superprocesses
zbMATH Keywords: weak convergence
zbMATH Keywords: Markov snakes
zbMATH Keywords: additive functionals
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01246334
OpenAlex ID: W2083939640
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 822727