Lyapunov Exponents for Nite State Nonlinear Ltering
نویسنده
چکیده
Consider the Wonham optimal ltering problem for a nite state ergodic Markov process in both discrete and continuous time, and let be the noise intensity for the observation. We examine the sensitivity of the solution with respect to the lter's initial conditions in terms of the gap between the rst two Lyapunov exponents of the Zakai equation for the unnormalized conditional probability. This gap is studied in the limit as ! 0 by techniques involving considerations of nonlinear ltering and the stochastic Feynman-Kac formula. Conditions are given for the limit to be either negative or ?1. Asymptotic bounds are derived in the latter case.
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