2009/10/26 by Nicolas Chopin, ChopinNicolas, Chopin, Nicolas +4
Computer Science · Mathematics · Physics and Astronomy · #60G35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Scientific Research and Discoveries #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks #math.PR #math.ST #msc:60G35 #stat.TH
paper · pdf · doi:10.48550/arxiv.0910.4870
arxiv created 2009/10/26 · openalex publication_date 2009/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but other models and algorithms of practical interest fall in this category. We study the asymptotic stability of such particle algorithms as time goes to infinity. As a corollary, practical conditions for the stability of the mixture Kalman filter, and a mixture GARCH filter, are derived. Finally, we show that our results can also lead to weaker conditions for the stability of standard particle algorithms, such that the potential function depends on the last state only.