Abstract
The paper deals with a possible approach to the problem of finite-dimensional filters in the nonlinear case, when the signal is a diffusion process and the observations are corrupted by additive white noise. The approach considers a sequence of finite-dimensional recursive filters that approximate the actual optimal one. The approximating filters are given in terms of functionals of continuous-time Markov chains that converge weakly to the original diffusion. These functionals can be recursively computed via a finite-dimensional Zakai equation, for which the solution is given in terms of a robust input-output relation.
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Communicated by S. K. Mitter
Work partially supported by the Consiglio Nazionale delle Ricerche (Italy) under Contract 79.00700.01.
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Di Masi, G.B., Runggaldier, W.J. Continuous-time approximations for the nonlinear filtering problem. Appl Math Optim 7, 233–245 (1981). https://doi.org/10.1007/BF01442118
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DOI: https://doi.org/10.1007/BF01442118