FILTERING SMOOTH SIGNALS FOR DIFFUSION OBSERVED PROCESS

Rafail KHASMINSKII

Wayne State University, Detroit
United States


ABSTRACT

Kalman type nonlinear filter is proposed for the estimation of unknown function S(t) with the known smoothness for the diffusion observed process. It is assumed that the drift coefficient of the observed process depends on S(t) and the diffusion coefficient is small, of order $\varepsilon$. The best possible rate of convergence risk to 0, as $\varepsilon$ tends to 0, is obtained. Analogous problem is considered for the case of partial observations.



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