Diffusions conditionnelles. II. Générateur conditionnel. Application au filtrage

Abstract

This paper is a continuation of “Diffusions conditionelles, I.” If ( x t , z t ) is a two-component diffusion process, it is shown that under appropriate conditions, the process x t ( t ⩽ T), given ( z s , s ⩽ T) is a nonhomogeneous strong Markov process, whose generator is explicitly found by using the theory of stochastic flows. The filtering equation is reduced to an ordinary partial differential equation.