Browsing by Author "Katzur, Ran"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Singular Perturbation and Order Reduction for Filtering Problem.(1987) Katzur, Ran; ISRWe consider the problem of optimal filtering of two dimensional diffusion process measured in a noisy channel. We approximate the solution of Zakai equation for the two dimensional process by a solution of Zakai equation for one dimensional process for two models. The first one is fast and slow variables, that is where one element of the process changes much more rapidly than the second one. The second model is the quasi-deterministic case for which the fast element has a small diffusion term. In both cases simple approximated equations for the filtering problem are given that make numerical solution simpler.Item Singular Perturbation Method for the Solution of Kushner's Equation.(1987) Katzur, Ran; ISRIn this paper we solve asymptotically Kushner's equation for the conditional probability density function of a one dimensional diffusion process measured in a low noise channel. We obtain the Stratonovich version and solve asymptotically this equation. The asymptotic aolution agrees with the asymptotic solution of Zakai's equation. In the second part of this paper we solve asymptotically Kushner's equation for a model of feedback channel and construct a sub-optimal filter for this model.