Evolution equations for Markov processes: Application to the white-noise theory of filtering
type: Item
instance of: scholarly article
title: Evolution equations for Markov processes: Application to the white-noise theory of filtering
zbMATH Open document ID: 0824.60075
DOI: 10.1007/BF01215995
published in: Applied Mathematics and Optimization
publication date: 1995-05-22T00:00:00Z
review text: Let \(X\) be a Markov process taking values in a complete separable metric space \(E\) and characterized via a martingale problem for an operator \(A\). The authors obtain a criterion for invariant measures when \(A\) is just a subset of continuous functions on \(E\). The authors then also prove uniqueness of the solutions to a measure-valued evolution equation. For the case of locally compact state space, similar results were developed by others [cf. \textit{P. E. Echeverria}, Z. Wahrscheinlichkeitstheorie Verw. Geb. 61, 1-16 (1982; Zbl 0476.60074); \textit{S. N. Ethier} and \textit{T. G. Kurtz}, ``Markov processes: Characterization and convergence'' (1986; Zbl 0592.60049), p. 252]. By applying authors' results to measure- valued filtering equation, uniqueness of the solutions to the analogue of the Zakai equation is proved in the class of all positive finite measures rather than only in a restricted class of measures.
reviewed by: Chengxun Wu
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 757767
zbMATH Keywords: Markov process
zbMATH Keywords: invariant measures
zbMATH Keywords: uniqueness of the solutions to a measure-valued evolution equation
zbMATH Keywords: measure-valued filtering equation
zbMATH Keywords: Zakai equation
author: Abhay G. Bhatt
author: Rajeeva L. Karandikar
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01215995
OpenAlex ID: W1990913039
description: scientific article; zbMATH DE number 757767