Approximate finite-dimensional filters for some nonlinear problems
Héctor J. Sussmann · Stochastics · 1982
We study the robust solutions of nonlinear filtering problems dX = dW, dY=[X+∊ƒ(X)]dt+dV, where ƒ is a polynomial, and ∊on a parameter. We show that, as ∊→0, the solution has an asymptotic series in powers of ∊, whose coefficients are outputs of finite-dimensional filters. This result had been suggested by Lie-algebraic calculations made by Hazewinkel. The proof given here is rigorous, and does not use Lie algebraic techniques.