Exponential stability in discrete-time filtering for non-ergodic signal.
type: Item
instance of: scholarly article
title: Exponential stability in discrete-time filtering for non-ergodic signal.
zbMATH Open document ID: 1056.93065
DOI: 10.1016/S0304-4149(99)00032-0
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: A discrete-time filtering model is considered where the signal and the observation process are given as follows: \[ X_n=a(X_{n-1})+b(X_{n-1})\xi _n,\quad n\geq 1 \] and \[ Y_n=X_n+\sigma \nu _n,\quad n\geq 1 \] where \(X_0\) is an \(\mathbb R^d\)-valued random variable and the coefficients \(a:\mathbb R^d\to \mathbb R^d\) and \(b:\mathbb R^d \to \mathbb R^{d\times d}\) are measurable maps. It is shown that, under appropriate conditions on coefficients, the total variation distance between the optimal filter and an incorrectly initialized filter converges to zero almost surely exponentially fast as time approaches infinity if \(\sigma \) is sufficiently small.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 1792521
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: asymptotic stability
zbMATH Keywords: discrete filtering
author: Amarjit Budhiraja
author: Daniel L. Ocone
MaRDI profile type: Publication
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Wikidata QID: Q127177216
full work available at URL: s0304-4149(99)00032-0
OpenAlex ID: W2095168080
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description: scientific article; zbMATH DE number 1792521