  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.
