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arXiv · 1112.2986

Dimensional reduction in nonlinear filtering: A homogenization approach

Peter Imkeller·N. Sri Namachchivaya·Nicolas Perkowski·Hoong C. Yeong
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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. 2011-12-13. Dimensional reduction in nonlinear filtering: A homogenization approach. https://doi.org/10.1214/12-aap901

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