An Adaptive Local Grid Refinement Method For Nonlinear Filtering
Zhiqiang Cai, François Le Gland, Huilong Zhang · 1995
: Numerical solution of the Zakai equation usually leads to large systems of equations which have to be solved at each time step. An algorithm for the numerical approximation of the Zakai equation is presented, based on discretization schemes provided by Kushner, and by LeGland. We use an a posteriori criterion based on truncation error, to localize refinement regions. We apply the fast adaptive composite grid (FAC) method introduced by McCormick for solving the resulting linear systems. Numerical tests are presented, which show the efficiency of the FAC method. Key-words: diffusion processes, nonlinear filtering, Zakai equation, stochastic PDE, multigrid methods, FAC. (R'esum'e : tsvp) This work was partially supported by the Commission of the European Communities, under the SCIENCE project SPDE's and Random Fields, project number SC1--CT91--0627, and by the Army Research Office, under grant DAAH04--95--1--0164. Center for Applied Mathematical Sciences, University of Southern Cali...