Markov chain approximations to filtering equations for reflecting diffusion processes.

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  • Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion 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 efficient, effective algorithm for implementing such filtering 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 efficiency of this new method to the previously developed branching particle filter and interacting particle filter methods. This Markov chain method is demonstrated to outperform the two-particle filter methods on our simulated test problem, which is motivated by the fish farming industry.

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    Article (Published)
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    © 2004 Stochastic Processes and their Applications. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited. Non-commercial use only.
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    • Michael A Kouritzin, Hongwei Long, Wei Sun, Markov chain approximations to filtering equations for reflecting diffusion processes, Stochastic Processes and their Applications, Volume 110, Issue 2, April 2004, Pages 275-294, ISSN 0304-4149,