Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Computers & Mathematics with Applications
Sparse Wiener chaos approximations of Zakai equation for nonlinear filtering
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Application of nonlinear filtering to credit risk
Operations Research Letters
A Multistage Wiener Chaos Expansion Method for Stochastic Advection-Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
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The objective of this paper is to develop an approach to nonlinear filtering based on the Cameron--Martin version of Wiener chaos expansion. This approach gives rise to a new numerical scheme for nonlinear filtering. The main feature of this algorithm is that it allows one to separate the computations involving the observations from those dealing only with the system parameters and to shift the latter off-line.