Journal of Applied Probability

On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions

Ajay Jasra

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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.

Article information

J. Appl. Probab., Volume 52, Number 2 (2015), 339-359.

First available in Project Euclid: 23 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 64C05
Secondary: 62F15: Bayesian inference

Particle filter central limit theorem smoothing


Jasra, Ajay. On the behaviour of the backward interpretation of Feynman-Kac formulae under verifiable conditions. J. Appl. Probab. 52 (2015), no. 2, 339--359. doi:10.1239/jap/1437658602.

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