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We investigate the robustness of nonlinear filtering for continuous timefinite state Markov chains, observed in white noise, with respect tomisspecification of the model parameters. It is shown that the distance betweenthe optimal filter and that with incorrect model parameters converges to zerouniformly over the infinite time interval as the misspecified model convergesto the true model, provided the signal obeys a mixing condition. The filteringerror is controlled through the exponential decay of the derivative of thenonlinear filter with respect to its initial condition. We allow simultaneouslyfor misspecification of the initial condition, of the transition rates of thesignal, and of the observation function. The first two cases are treated byrelatively elementary means, while the latter case requires the use ofSkorokhod integrals and tools of anticipative stochastic calculus.

Model robustness of finite state nonlinear filtering over the infinite time horizon