Nonlinear Filtering and Large Deviations: A PDE-Control Theoretic Approach

M.R. James and J.S. Baras

Stochastics, Vol. 23, pp. 391-412, 1988.

Abstract

We consider the nonlinear filtering problem dx = f(x)dt + √(є)dw, dy = h(x)dt + √(є)dv, and obtain lim[є→0] є log q^є (x,t) = -W(x,t) for unnormalized conditional densities q^є (x,t) using PDE methods. Here, W(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation and is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation.