Moderate deviations for particle filtering

• 成果类型: Article
• 署名作者: Doug, R; Guillin, A; Najim, J
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; IMT Atlantique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000657
• 发表日期: 2005
• 页码: 587-614
• 关键词: systems; sums

摘要

Consider the state space model (X-t, Y-t), where (X-t) is a Markov chain, and (Y-t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X-t\Y-1,..., Y-t), the law of X-t given the observations (Y-1,..., Y-t). The particle filtering method gives an approximation of the law L(X-t\Y-1,..., Y-t) by an empirical measure 1/n Sigma(1)(n)delta(xi,t). In this paper we establish the moderate deviation principle for the empirical mean 1/n Sigma(1)(n)psi(x(i,t)) (centered and properly resealed) when the number of particles grows to infinity, enhancing the central limit theorem. Several extensions and examples are also studied.