  We investigate the robustness of nonlinear filtering for continuous time
finite state Markov chains, observed in white noise, with respect to
misspecification of the model parameters. It is shown that the distance between
the optimal filter and that with incorrect model parameters converges to zero
uniformly over the infinite time interval as the misspecified model converges
to the true model, provided the signal obeys a mixing condition. The filtering
error is controlled through the exponential decay of the derivative of the
nonlinear filter with respect to its initial condition. We allow simultaneously
for misspecification of the initial condition, of the transition rates of the
signal, and of the observation function. The first two cases are treated by
relatively elementary means, while the latter case requires the use of
Skorokhod integrals and tools of anticipative stochastic calculus.
