Asymptotic stability of the Wonham filter: Ergodic and nonergodic signals

Peter Baxendale*, Pavel Chigansky, Robert Liptser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


The stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability rates, which do not depend on the observations. In the nonergodic case, the stability is implied by identiflability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure.

Original languageAmerican English
Pages (from-to)643-669
Number of pages27
JournalSIAM Journal on Control and Optimization
Issue number2
StatePublished - 2005
Externally publishedYes


  • Nonlinear filtering
  • Stability
  • Wonham filter


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