## Approximation and Limit Results for Nonlinear Filters over an Infinite Time Interval: Part II, Random Sampling Algorithms (0)

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@MISC{Budhiraja_approximationand,

author = {Amarjit Budhiraja and Harold J. Kushner},

title = {Approximation and Limit Results for Nonlinear Filters over an Infinite Time Interval: Part II, Random Sampling Algorithms},

year = {}

}

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### Abstract

The paper is concerned with approximations to nonlinear filtering problems that are of interest over a very long time interval. Since the optimal filter can rarely be constructed, one needs to compute with numerically feasible approximations. The signal model can be a jump-diffusion, reflected or not. The observations can be taken either in discrete or continuous time. The cost of interest is the pathwise error per unit time over a long time interval. In a previous paper of the authors [2], it was shown, under quite reasonable conditions on the approximating filter and on the signal and noise processes that (as time, 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 just what one would get if the approximating processes were replaced by their ideal values and the optimal filter were used. When suitable approximating filters cannot be readily constructed due to excessive computational requirem...