## The Annals of Applied Probability

### Dimensional reduction in nonlinear filtering: A homogenization approach

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 22 October 2013

https://projecteuclid.org/euclid.aoap/1382447689

Digital Object Identifier
doi:10.1214/12-AAP901

Mathematical Reviews number (MathSciNet)
MR3127936

Zentralblatt MATH identifier
1288.60049

#### Citation

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. https://projecteuclid.org/euclid.aoap/1382447689

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