A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Pavel Chigansky, Ramon Van Handel

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2318-2345
Number of pages28
JournalAnnals of Applied Probability
Volume20
Issue number6
DOIs
StatePublished - Dec 1 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic stability
  • Filtering
  • Hidden Markov models
  • Unique ergodicity

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