No abstract

No abstract

No abstract

No 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. S = a 1 1 , . . . , a 1 n1 S1 , . . . , a m 1 , . . . , a m nm Sm , where the subalphabets S 1 , . . . , S m are noncommunicating in the sense that for any i = j and t ≥ sSo, unless m = 1, X t is a compound Markov chain with the transition intensities *