STABILITY PROPERTIES OF SOME PARTICLE FILTERS

• 成果类型: Article
• 署名作者: Whiteley, Nick
• 署名单位: University of Bristol
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP909
• 发表日期: 2013
• 页码: 2500-2537
• 关键词: CENTRAL-LIMIT-THEOREM; nonlinear filters; approximation; variance; bounds

摘要

Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic, relative variance associated with a particle approximation of the normalizing constant is bounded linearly in time. The conditions are demonstrated to hold for some hidden Markov models on noncompact state spaces. The particle stability results are obtained by proving v-norm multiplicative stability and exponential moment results for the underlying Feynman-Kac formulas.