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Monte Carlo methods for backward equations in nonlinear filtering

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic analysis Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  01 July 2016

G. N. Milstein  and
M. V. Tretyakov
G. N. Milstein*
Affiliation:
Ural State University
M. V. Tretyakov*
Affiliation:
University of Leicester
*
∗ Postal address: Ural State University, Lenin Street 51, 620083 Ekaterinburg, Russia. Email address: grigori.milstein@usu.ru
∗∗ Postal address: Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK. Email address: m.tretyakov@le.ac.uk
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Abstract

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We consider Monte Carlo methods for the classical nonlinear filtering problem. The first method is based on a backward pathwise filtering equation and the second method is related to a backward linear stochastic partial differential equation. We study convergence of the proposed numerical algorithms. The considered methods have such advantages as a capability in principle to solve filtering problems of large dimensionality, reliable error control, and recurrency. Their efficiency is achieved due to the numerical procedures which use effective numerical schemes and variance reduction techniques. The results obtained are supported by numerical experiments.

Keywords

Pathwise filtering equationstochastic partial differential equationMonte Carlo techniqueKallianpur–Striebel formulamean-square and weak numerical methods

MSC classification

Primary: 93E11: Filtering 65C30: Stochastic differential and integral equations 60G35: Signal detection and filtering 60H35: Computational methods for stochastic equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 1 , March 2009 , pp. 63 - 100
Copyright
Copyright © Applied Probability Trust 2009 

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