June 2015 On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions
Ajay Jasra
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J. Appl. Probab. 52(2): 339-359 (June 2015). DOI: 10.1239/jap/1437658602

Abstract

We consider the time behaviour associated to the sequential Monte Carlo estimate of the backward interpretation of Feynman-Kac formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models. We prove a central limit theorem under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression for additive functionals grows at most linearly in time under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some hidden Markov models.

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Ajay Jasra. "On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions." J. Appl. Probab. 52 (2) 339 - 359, June 2015. https://doi.org/10.1239/jap/1437658602

Information

Published: June 2015
First available in Project Euclid: 23 July 2015

zbMATH: 1327.62036
MathSciNet: MR3372079
Digital Object Identifier: 10.1239/jap/1437658602

Subjects:
Primary: 64C05
Secondary: 62F15

Keywords: central limit theorem , particle filter , smoothing

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 2 • June 2015
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