Optimal Filtering for HMM Governed by Special Jump Processes

The paper presents a solution of optimal filtering problem for stochastic differential systems of random structure with switches generated by a special class of Markov jump processes. The equations for both the conditional expectation of some signal process given a noisy observation, and conditional probability density function (pdf) are obtained. Numerical methods for solution of corresponding Fokker-Plank and Zakai equation analogues are given and illustrated by an example.