Monte Carlo Algorithms and Asymptotic Problems in Nonlinear Filtering

We are concerned with numerically feasible approximations to nonlinear filtering problems, which are of interest over a very long time interval. The cost of concern is the pathwise error per unit time. In [4], it was shown, under reasonable conditions, that (as time, noise bandwidth, process and filter approximation, etc.) go to their limit in any way at all, the limit of the pathwise average costs per unit time is what one gets with the optimal filter. When good approximations cannot be constructed due to excessive computational requirements, approximations based on random sampling methods (or, perhaps, combinations of sampling and analytical methods) become attractive. Extensions of the previous work to a wide class of such algorithms is dealt with, with similar results. For brevity, we confine ourselves to discrete time, but the same results hold for the continuous time case [5].

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