On uniqueness and weak convergence of solutions for the stochastic differential equations of nonlinear filtering

Abstract

This thesis is a contribution to the theory of nonlinear filtering, and is concerned with two basic issues. The first of these deals with pathwise uniqueness and uniqueness in law for solutions of the measure-valued stochastic differential equations of nonlinear filtering, in the case where there is genuine dependence of the signal on the observation process. The second issue uses this uniqueness to establish convergence of nonlinear filters corresponding to a class of dynamical systems governed by sigularly perturbed stochastic differential equations, in which the perturbation is wide-band random process with certain ergodic properties.