An ergodic theorem for filtering with applications to stability

Details An ergodic theorem for filtering with applications to stability An ergodic theorem for filtering with applications to stability

2004-04-28

arxiv.org/abs/math/0404515v2

Systems & Control Letters, Volume 55, Issue 11, November 2006, Pages 908-917

Mathematics

Probability

The final version to appear in Syst. Contr. Letters after a substantial revision

Scientific paper

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.

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