A COMPLETE SOLUTION TO BLACKWELL'S UNIQUE ERGODICITY PROBLEM FOR HIDDEN MARKOV CHAINS

• 成果类型: Article
• 署名作者: Chigansky, Pavel; van Handel, Ramon
• 署名单位: Hebrew University of Jerusalem; Princeton University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP688
• 发表日期: 2010
• 页码: 2318-2345
• 关键词: Asymptotic stability; filter; observability; signals; models

摘要

We develop necessary and sufficient conditions for uniqueness of the invariant measure of the filtering process associated to an ergodic hidden Markov model in a finite or countable state space. These results provide a complete solution to a problem posed by Blackwell (1957), and subsume earlier partial results due to Kaijser, Kochman and Reeds. The proofs of our main results are based on the stability theory of nonlinear filters.