The stability of conditional Markov processes and Markov chains in random environments
By Ramon van Handel. 2008
65 citations recorded by the source corpus.
We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of σ-fields, which is key for the stability of the nonlinear filter and partially resolves a long-standing gap in the proof of a result of Kunita [J. Multivariate Anal. 1 (1971) 365―393]. A similar result is obtained also in the continuous time setting. The proofs are based on an ergodic theorem for Markov chains in random environments in a general state space.
Subfields: Control and Systems Engineering, Management Information Systems, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3731ee616002762de690eb08656cc934556d7435
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In Control and Systems Engineering
In Management Information Systems
In Statistics and Probability
- Jimmy Olsson
- Randal Douc
- Eric Moulines
- Ramon van Handel
- Gareth O. Roberts
- Francis R. Bach
- Arnaud Guillin
- Fredrik Lindsten
Citations in the corpus
- Uniform time average consistency of Monte Carlo particle filters (2008, background): “Let us remark that the Markov property is elementary, while uniqueness of the invariant measure hinges on recent progress on the filter stability problem [29].”
- Long-term stability of sequential Monte Carlo methods under verifiable conditions (2012, background): “A first breakthrough toward stability results for noncompact state spaces was made in [34].”