Nonlinear filtering algorithms based on averaging over characteristics and on the innovation approach.
Seminar Room 1, Newton Institute
It is well known that numerical methods for nonlinear filtering problems, which directly use the Kallianpur-Striebel formula, can exhibit computational instabilities due to the presence of very large or very small exponents in both the numerator and denominator of the formula. We obtain computationally stable schemes by exploiting the innovation approach. We propose Monte Carlo algorithms based on the method of characteristics for linear parabolic stochastic partial differential equations. Convergence and some properties of the considered algorithms are studied. Variance reduction techniques are discussed. Results of some numerical experiments are presented. The talk is based on a joint work with G.N. Milstein.