Forgetting of the initial condition for the filter in general state-space hidden Markov chain: A coupling approach

Randal Douc, Eric Moulines, Ya’acov Ritov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We give simple conditions that ensure exponential forgetting of the initial conditions of the filter for general state-space hidden Markov chain. The proofs are based on the coupling argument applied to the posterior Markov kernels. These results are useful both for filtering hidden Markov models using approximation methods (e.g., particle filters) and for proving asymptotic properties of estimators. The results are general enough to cover models like the Gaussian state space model, without using the special structure that permits the application of the Kalman filter.

Original languageEnglish
Pages (from-to)27-49
Number of pages23
JournalElectronic Journal of Probability
Volume14
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Coupling
  • Hidden Markov chain
  • Non-linear filtering
  • Stability

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