Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
type: Item
instance of: scholarly article
title: Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering
zbMATH Open document ID: 0861.60051
author: Gopinath Kallianpur
author: Abhay G. Bhatt
author: Rajeeva L. Karandikar
published in: The Annals of Probability
publication date: 1997-04-22T00:00:00Z
review text: After an introduction, in the second part of the paper some necessary preliminary results are presented. The main section of the article is the third one. Here, assuming that the signal process which is a Markov one, takes values in a complete separable metric space, pathwise uniqueness of solution of the Zakai equation under a set of conditions is proved. In Section 4, an important special case of independent signal and noise is presented. The extension to the infinite dimensions is done in Section 5. Applying the results to signals taking values in Hilbert space, in Section 6 this can be done to models of environmental pollution. In Section 7, results are applied to a signal which is modelled by a semilinear stochastic differential equation on a Hilbert space. In the last two parts the statistical robustness is analyzed.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 897281
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: Zakai equation
zbMATH Keywords: martingale problem
zbMATH Keywords: robustness
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176987808
OpenAlex ID: W2025416790
DOI: 10.1214/AOP/1176987808
description: scientific article; zbMATH DE number 897281