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Numerical solution for a class of SPDEs over bounded domains

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Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295–308].
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Keywords: 35R60; 60H15; 60K35; 93E11; Kushner–FKK equation; diffusions with reflecting boundary; interacting particle systems; nonlinear filtering; stochastic partial differential equations

Document Type: Research Article

Affiliations: 1: Department of Mathematics, Imperial College London, 180 Queen's Gate, London,SW7 2BZ, UK 2: Department of Mathematics, University of Tennessee, Knoxville, TN,37996-1300, USA

Publication date: May 4, 2014

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