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Monte Carlo methods for backward equations in nonlinear filtering

  • G. N. Milstein (a1) and M. V. Tretyakov (a2)

Abstract

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.

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Corresponding author

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

References

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Monte Carlo methods for backward equations in nonlinear filtering

  • G. N. Milstein (a1) and M. V. Tretyakov (a2)

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