An ergodic theorem for filtering with applications to stability

Pavel Chigansky

doi:10.1016/j.sysconle.2006.06.001

An ergodic theorem for filtering with applications to stability

Pavel Chigansky^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Ergodic properties of the signal-filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the stability problem of the nonlinear filter with respect to initial conditions. The Furstenberg-Khasminskii formula is derived for the top Lyapunov exponent of the Zakai equation and is used to estimate the stability index of the filter.

Original language	English
Pages (from-to)	908-917
Number of pages	10
Journal	Systems and Control Letters
Volume	55
Issue number	11
DOIs	https://doi.org/10.1016/j.sysconle.2006.06.001
State	Published - Nov 2006
Externally published	Yes

Keywords

Ergodic theorem
Lyapunov exponents
Nonlinear filtering
Stability

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10.1016/j.sysconle.2006.06.001

Cite this

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abstract = "Ergodic properties of the signal-filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the stability problem of the nonlinear filter with respect to initial conditions. The Furstenberg-Khasminskii formula is derived for the top Lyapunov exponent of the Zakai equation and is used to estimate the stability index of the filter.",

keywords = "Ergodic theorem, Lyapunov exponents, Nonlinear filtering, Stability",

author = "Pavel Chigansky",

year = "2006",

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AB - Ergodic properties of the signal-filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the stability problem of the nonlinear filter with respect to initial conditions. The Furstenberg-Khasminskii formula is derived for the top Lyapunov exponent of the Zakai equation and is used to estimate the stability index of the filter.

KW - Ergodic theorem

KW - Lyapunov exponents

KW - Nonlinear filtering

KW - Stability

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JO - Systems and Control Letters

JF - Systems and Control Letters

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An ergodic theorem for filtering with applications to stability

Abstract

Keywords

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