The Annals of Applied Probability

Dimensional reduction in nonlinear filtering: A homogenization approach

Peter Imkeller, N. Sri Namachchivaya, Nicolas Perkowski, and Hoong C. Yeong

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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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Ann. Appl. Probab., Volume 23, Number 6 (2013), 2290-2326.

First available in Project Euclid: 22 October 2013

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Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 60H15: Stochastic partial differential equations [See also 35R60] 60H35: Computational methods for stochastic equations [See also 65C30]

Nonlinear filtering dimensional reduction homogenization particle filtering asymptotic expansion SPDE BDSDE


Imkeller, Peter; Namachchivaya, N. Sri; Perkowski, Nicolas; Yeong, Hoong C. Dimensional reduction in nonlinear filtering: A homogenization approach. Ann. Appl. Probab. 23 (2013), no. 6, 2290--2326. doi:10.1214/12-AAP901.

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