Uniqueness for Measure-Valued Equations of Nonlinear Filtering for Stochastic Dynamical Systems with L\'evy Noises

Abstract

In the article, Zakai and Kushner-Stratonovich equations of the nonlinear filtering problem for a non-Gaussian signal-observation system are considered. Moreover, we prove that under some general assumption, the Zakai equation has pathwise uniqueness and uniqueness in joint law, and the Kushner-Stratonovich equation is unique in joint law.