## Asymptotic stability of the Wonham filter: ergodic and nonergodic signals

Venue: | SIAM J. Control Optim |

Citations: | 25 - 13 self |

### BibTeX

@ARTICLE{Baxendale_asymptoticstability,

author = {Peter Baxendale and Pavel Chigansky and Robert Liptser},

title = {Asymptotic stability of the Wonham filter: ergodic and nonergodic signals},

journal = {SIAM J. Control Optim},

year = {},

pages = {643--669}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. 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 non-ergodic case, the stability is implied by identifiability conditions, formulated explicitly in terms of the transition intensities matrix and the observation structure. Key words. Nonlinear filtering, stability, Wonham filter