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Lyapunov exponents for finite state nonlinear filtering. (English) Zbl 0940.93073

From the authors’ abstract: “Consider the Wonham filtering problem for a finite state ergodic Markov process in both discrete and continuous time. We examine the sensitivity of the solution with respect to the filter’s initial conditions in terms of the gap between the first two Lyapunov exponents of the Zakai equation for the unnormalized conditional probability. This gap is studied for vanishing noise intensity for the observation by techniques involving considerations of nonlinear filtering and the stochastic Feynman-Kac formula”.

MSC:

93E11 Filtering in stochastic control theory
60J57 Multiplicative functionals and Markov processes
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
93B35 Sensitivity (robustness)
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