The problem of Nonlinear Filtering is to estimate the state of a nonlinear stochastic dynamical system given nosy observations . In the linear situation the problems arose in the work of Wiener , Kolmogoroff in the 40’s and subsequently in the work of Kalman in late fifties and early sixties . One of the major applications of this theory is for weather prediction where the problem is known as Data Assimilation. In this lecture I discuss the connection of this work to Shannon Information Theory and Nonequilibrium Statistical Mechanics.
Joint work with Nigel Newton