Markov chain approximations to filtering equations for reflecting diffusion processes. (Q2574641)

Markov chain approximations to the Duncan-Mortensen-Zakai SPDE for the unnormalized density in the filtering problem on regular, bounded domains are studied. The signal process is a diffusion reflected on the boundary of a \(d\)-dimensional rectangle, with a symmetrizable generator. The approximating Markov chains are based on a wide band observation noise approximation, dividing the signal state space into cells and utilizing an empirical measure process estimation. The convergence of approximations to the conditional density has been proven and the computational efficiency of the method has been compared to previously developed branching particle filter and interacting particle filter methods by means of simulations.