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Issue ESAIM: Proc.
Volume 19, 2007
Conference Oxford sur les méthodes de Monte Carlo séquentielles
Page(s) 121 - 125
DOI http://dx.doi.org/10.1051/proc:071916
Published online 30 October 2007

ESAIM: Proc., 2007, Vol. 19, pp. 121-125
DOI: 10.1051/proc:071916

Numerical solutions for a class of SPDEs over bounded domains

Dan Crisan1 and Jie Xiong2, 3

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
3  Department of Mathematics, Hebei Normal University, Shijiazhuang 050016, PRC


(Published online: 30 October 2007)

Abstract
The optimal filter for a bounded signal with reflecting boundary is approximated by the (un-weighted) empirical measure of a finite interacting particle system. The main motivation of this un-weighted empirical measure representation is to overcome the slow convergence rate of the weighted one because of the exponential growth of the variance of individual weight of the particle. The finite system of SDEs with reflecting boundary is then solved numerically by Euler scheme.


Mathematics Subject Classification. 60H15, 60K35, 35R60, 93E11

Key words: Stochastic partial differential equation, particle system approximation, diffusion with reflecting boundary, Kushner-FKK equation, nonlinear filtering


© EDP Sciences, ESAIM 2007


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