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Long-term stability of sequential monte carlo methods under verifiable conditions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-0772-846X
2014 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 24, no 5, 1767-1802 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 24, no 5, 1767-1802 p.
Keyword [en]
Asymptotic variance, general hidden Markov models, local Doeblin condition, bootstrap particle filter, sequential Monte Carlo methods, time uniform convergence
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-149959DOI: 10.1214/13-AAP962ISI: 000339705200001Scopus ID: 2-s2.0-84903946744OAI: oai:DiVA.org:kth-149959DiVA: diva2:744914
Funder
Swedish Research Council, 2011-5577
Note

QC 20140909

Available from: 2014-09-09 Created: 2014-08-29 Last updated: 2017-12-05Bibliographically approved

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Olsson, Jimmy

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