DIMENSIONAL REDUCTION IN NONLINEAR FILTERING: A HOMOGENIZATION APPROACH

• 成果类型: Article
• 署名作者: Imkeller, Peter; Namachchivaya, N. Sri; Perkowski, Nicolas; Yeong, Hoong C.
• 署名单位: Humboldt University of Berlin; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP901
• 发表日期: 2013
• 页码: 2290-2326
• 关键词: diffusion-approximation; Poisson equation

摘要

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 root epsilon. 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.