2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64124Stability 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.27 pagesProbabilityOptimization and Control93E11; 60J57text