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An Approximation for the Zakai Equation |
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| Authors: | Y. Hu G. Kallianpur J. Xiong |
| Affiliation: | (1) Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142, USA hu@math.ukans.edu, US;(2) Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA gk@stat.unc.edu, US;(3) Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA jxiong@math.utk.edu, US |
| Abstract: | In this article we consider a polygonal approximation to the unnormalized conditional measure of a filtering problem, which is the solution of the Zakai stochastic differential equation on measure space. An estimate of the convergence rate based on a distance which is equivalent to the weak convergence topology is derived. We also study the density of the unnormalized conditional measure, which is the solution of the Zakai stochastic partial differential equation. An estimate of the convergence rate is also given in this case. 60F25, 60H10.} Accepted 23 April 2001. Online publication 14 August 2001. |
| Keywords: | . Filtering Zakai equation Stochastic differential equation Weak convergence. AMS Classification. Primary 60G35 93E11 Secondary 60F25 60H10. |
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