Markov chain approximations to #ltering equations for re(ecting di)usion processes
Michael A. Kouritzin, Hongwei Long, Wei Sun · 2004
Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear #ltering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to re(ecting di)usion signals with symmetrizable generators. Our Markov chains are constructed by employing a wide band observation noise approximation, dividing the signal state space into cells, and utilizing an empirical measure process estimation. The upshot of our approximation is an e<cient, e)ective algorithm for implementing such #ltering problems. We prove that our approximations converge to the desired conditional distribution of the signal given the observation. Moreover, we use simulations to compare computational ef#ciency of this new method to the previously developed branching particle #lter and interacting particle #lter methods. This Markov chain method is demonstrated to outperform the two-particle #lter methods on our simulated test problem, which is motivated by the #sh farming industry. c