Forgetting of the initial distribution for nonergodic hidden Markov chains

DOI10.1214/09-AAP632zbMath1197.93158OpenAlexW2014170832MaRDI QIDQ1958495

Randal Douc, Eric Moulines, Benoit Landelle, Elisabeth Gassiat

Publication date: 4 October 2010

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/09-aap632

zbMATH Keywords

nonlinear filteringFeynman-Kac semigroupforgetting of the initial distributionnonergodic hidden Markov chains

Mathematics Subject Classification ID

Bayesian problems; characterization of Bayes procedures (62C10) Filtering in stochastic control theory (93E11) Discrete-time Markov processes on general state spaces (60J05) Signal detection and filtering (aspects of stochastic processes) (60G35)

Related Items (4)

Exponential filter stability via Dobrushin's coefficient ⋮ Dimension-free Wasserstein contraction of nonlinear filters ⋮ Exponential forgetting of smoothing distributions for pairwise Markov models ⋮ Uniform time average consistency of Monte Carlo particle filters

Cites Work

• A note on exponential stability of the nonlinear filter for denumerable Markov chains
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• Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
• Uniform observability of hidden Markov models and filter stability for unstable signals
• A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals.
• Sequential Monte Carlo Methods in Practice
• Stability of the discrete time filter in terms of the tails of noise distributions
• Asymptotic Stability of the Optimal Filter with Respect to Its Initial Condition
• Stability and Uniform Particle Approximation of Nonlinear Filters in Case of Non Ergodic Signals
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