Chapter2001

Numerical Solutions for a Class of SPDEs with Application to Filtering

31 citations0/0 files storedBirkhäuser Boston eBooks

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Stochastic processes and financial applications Target Tracking and Data Fusion in Sensor Networks Numerical methods for differential equations

Abstract

A simulation scheme for a class of nonlinear stochastic partial differential equations is proposed and error bounds for the scheme are derived. The scheme is based on the fact that the solutions of the SPDEs can be represented by the weighted empirical measure of an infinite system of interacting particles. There are two sources of error in the scheme, one due to finite sampling of the infinite collection of particles and the other due to the Euler scheme used in the simulation of the individual particle motions. The error bounds take into account both sources of error. The results can be applied to nonlinear filtering problems.

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References

2016Numerical solution of stochastic differential equations 1997Stochastic Analysis 1977Probability Methods for Approximations in Stochastic Control and for Elliptic Equations 1991Time-discretization of the zakai equation for diffusion processes observed in correlated noise

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