FORGETTING OF THE INITIAL DISTRIBUTION FOR NONERGODIC HIDDEN MARKOV CHAINS

• 成果类型: Article
• 署名作者: Douc, Randal; Gassiat, Elisabeth; Landelle, Benoit; Moulines, Eric
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite Paris Saclay; Thales Group; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP632
• 发表日期: 2010
• 页码: 1638-1662
• 关键词: uniform particle approximation; exponential stability; nonlinear filters; models

摘要

In this paper, the forgetting of the initial distribution for a nonergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the filter. Both a pathwise and mean convergence of the total variation distance of the filter started from two different initial distributions are obtained. The results are illustrated using a generic nonergodic state-space model for which both pathwise and mean exponential stability is established.