An ergodic theorem for filtering with applications to stability

Pavel Chigansky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageAmerican English
Pages (from-to)908-917
Number of pages10
JournalSystems and Control Letters
Issue number11
StatePublished - Nov 2006
Externally publishedYes


  • Ergodic theorem
  • Lyapunov exponents
  • Nonlinear filtering
  • Stability


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