Robustness and Convergence of Approximations to Nonlinear Filters for Jump-Diffusions

The paper treats numerical approximations to the nonlinear ltering problem for jump{diiusion processes. This is a key problem in stochastic systems analysis. The processes are deened, and the optimal lters described. In the general nonlinear case, the optimal lters cannot be computed, and some numerical approximation is needed. Then the weak conditions that are required for the convergence of the approximations are given and the convergence is proved. Examples of useful approximations which satisfy the conditions are given. Quite weak conditions are given under which the approximating lter is continuous in the observation function, and it is shown that our canonical methods satisfy the conditions. Such continuity is essential if the approximations are to be used with conndence on actual physical data. Finally, we prove the convergence of monte carlo methods for approximating the optimal lters, and also show that the optimal lter is continuous in the parameters of the signal model.

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