Dimensional reduction in nonlinear filtering: A homogenization approach

Peter Imkeller; N. Sri Namachchivaya; Nicolas Perkowski; Hoong C. Yeong

doi:10.1214/12-AAP901

Dimensional reduction in nonlinear filtering: A homogenization approach

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

Research output: Contribution to journal › Article › peer-review

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 √ ε. 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.

Original language	English (US)
Pages (from-to)	2290-2326
Number of pages	37
Journal	Annals of Applied Probability
Volume	23
Issue number	6
DOIs	https://doi.org/10.1214/12-AAP901
State	Published - Dec 2013
Externally published	Yes

Keywords

Asymptotic expansion
BDSDE
Dimensional reduction
Homogenization
Nonlinear filtering
Particle filtering
SPDE

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/12-AAP901

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AU - Perkowski, Nicolas

AU - Yeong, Hoong C.

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KW - Asymptotic expansion

KW - BDSDE

KW - Dimensional reduction

KW - Homogenization

KW - Nonlinear filtering

KW - Particle filtering

KW - SPDE

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ER -

Dimensional reduction in nonlinear filtering: A homogenization approach

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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