Exponential forgetting and geometric ergodicity in hidden Markov models
type: Item
instance of: scholarly article
title: Exponential forgetting and geometric ergodicity in hidden Markov models
zbMATH Open document ID: 0941.93053
DOI: 10.1007/PL00009861
author: Laurent Mevel
author: François Le Gland
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2000-07-24T00:00:00Z
review text: This paper considers a hidden Markov model with multidimensional observations, and with misspecification, i.e., the assumed coefficients (transition probability matrix and observation conditional densities) are possibly different from the true coefficients. Under mild assumptions on the coefficients of both the true and the assumed models, it is proved that: (i) the prediction filter, and its gradient with respect to some parameter in the model, forget almost surely their initial condition exponentially fast, and (ii) the extended Markov chain, whose components are the unobserved Markov chain, the observation sequence, the prediction filter, and its gradient, is geometrically ergodic and has a unique invariant probability distribution.
reviewed by: Vyacheslav A. Vasiliev
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 15B52
zbMATH DE Number: 1428467
zbMATH Keywords: hidden Markov models
zbMATH Keywords: misspecified model
zbMATH Keywords: prediction filter
zbMATH Keywords: exponential forgetting
zbMATH Keywords: product of random matrices
MaRDI profile type: Publication
full work available at URL: pl00009861
OpenAlex ID: W2157721994
description: scientific article; zbMATH DE number 1428467