LONG-TERM STABILITY OF SEQUENTIAL MONTE CARLO METHODS UNDER VERIFIABLE CONDITIONS

• 成果类型: Article
• 署名作者: Douc, Randal; Moulines, Eric; Olsson, Jimmy
• 署名单位: Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique; Royal Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP962
• 发表日期: 2014
• 页码: 1767-1802
• 关键词: uniform particle approximation; nonlinear filters; asymptotic properties; systems

摘要

This paper discusses particle filtering in general hidden Markov models (HMMs) and presents novel theoretical results on the long-term stability of bootstrap-type particle filters. More specifically, we establish that the asymptotic variance of the Monte Carlo estimates produced by the bootstrap filter is uniformly bounded in time. On the contrary to most previous results of this type, which in general presuppose that the state space of the hidden state process is compact (an assumption that is rarely satisfied in practice), our very mild assumptions are satisfied for a large class of HMMs with possibly non-compact state space. In addition, we derive a similar time uniform bound on the asymptotic L-p error. Importantly, our results hold for misspecified models; that is, we do not at all assume that the data entering into the particle filter originate from the model governing the dynamics of the particles or not even from an HMM.