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December 2013 Dimensional reduction in nonlinear filtering: A homogenization approach
Peter Imkeller, N. Sri Namachchivaya, Nicolas Perkowski, Hoong C. Yeong
Ann. Appl. Probab. 23(6): 2290-2326 (December 2013). DOI: 10.1214/12-AAP901

Abstract

We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate $\sqrt{\varepsilon}$. This is achieved by a suitable asymptotic expansion of the dual of the Zakai equation, and by probabilistically representing the correction terms with the help of BDSDEs.

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Peter Imkeller. N. Sri Namachchivaya. Nicolas Perkowski. Hoong C. Yeong. "Dimensional reduction in nonlinear filtering: A homogenization approach." Ann. Appl. Probab. 23 (6) 2290 - 2326, December 2013. https://doi.org/10.1214/12-AAP901

Information

Published: December 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1288.60049
MathSciNet: MR3127936
Digital Object Identifier: 10.1214/12-AAP901

Subjects:
Primary: 35B27, 60G35, 60H15, 60H35

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 6 • December 2013
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