On filtering for a hidden Markov chain under square performance criterion
type: Item
instance of: scholarly article
title: On filtering for a hidden Markov chain under square performance criterion
zbMATH Open document ID: 0969.93041
published in: Problems of Information Transmission
publication date: 2001-10-04T00:00:00Z
review text: Let \(\theta(t)\) be a nonobservable Markov chain with discrete time and with a finite number of states \(\{a_1,\dots, a_n\}\). Let the conditional distribution of the observations \(X_t\in \mathbb{R}^d\) be \({\mathbf P}\{X_t\leq x\mid \theta(t)\}= F_{\theta(t)}(x)\), where \(F_{a_1}(x),\dots, F_{a_n}(x)\) are known distribution functions in \(\mathbb{R}^d\). The problem of filtering consists in the reconstruction of \(\theta(t)\) from the observations \(X_k\), \(k\leq t\). In the case of a Markov chain with rate transitions, an asymptotic formula for the mean-square error of the optimal filter is obtained.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 1551598
zbMATH Keywords: Markov chain
zbMATH Keywords: filtering
zbMATH Keywords: rate transitions
zbMATH Keywords: asymptotic formula
zbMATH Keywords: mean-square error
author: Yu. Golubev
reviewed by: Grigori N. Milstein
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1551598