Filtering of stochastic nonlinear wave equations

.In this article, we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider both stochastic calculus and white noise filtering methods and derive measure-valued evolution equations for the nonlinear filter and prove existence and uniqueness theorems for the solutions. We will also study first-order approximations to these measure-valued evolutions by linearizing the wave equations and characterize the filter dynamics in terms of infinite-dimensional operator Riccati equations and establish solvability theorems.