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

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

2006-04-12

arxiv.org/abs/math/0604295v3

Annals of Applied Probability 2007, Vol. 17, No. 2, 688-715

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000871 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000871

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.

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