Real time solution of Duncan-Mortensen-Zakai equation without memory

Stephen S-T Yau Shing-Tung Yau

Analysis of PDEs mathscidoc:1912.43719

5086-5091, 2008.12
It is well known that the nonlinear filtering problem has important applications in both military and commercial industries. The central problem of nonlinear filtering is to solve the DMZ equation in real time and memoryless manner. The purpose of this paper is to show that, under very mild conditions (which essentially say that the growth of the observation |h| is greater than the growth of the drift |f|), the DMZ equation admits a unique nonnegative weak solution u which can be approximated by a solution u<sub>R</sub> of the DMZ equation on the ball B<sub>R</sub> with u<sub>R</sub>|<sub>BR</sub> = 0. The error of this approximation is bounded by a function of R which tends to zero as R goes to infinity. The solution u<sub>R</sub> can in turn be approximated efficiently by an algorithm depending only on solving the observation-independent Kolmogorov equation on B<sub>R</sub>. In theory, our algorithm can solve basically all engineering problems in real time manner. Specifically
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  title={Real time solution of Duncan-Mortensen-Zakai equation without memory},
  author={Stephen S-T Yau, and Shing-Tung Yau},
Stephen S-T Yau, and Shing-Tung Yau. Real time solution of Duncan-Mortensen-Zakai equation without memory. 2008. pp.5086-5091.
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