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A Functional Central Limit Theorem for a Class of Interacting Markov
Chain Monte Carlo Methods
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Bernard Bercu, INRIA et Institut de Mathématiques de Bordeaux
Pierre Del Moral, INRIA et Institut de Mathématiques de Bordeaux
Arnaud Doucet, University of
British Columbia
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Abstract
We present a functional central limit theorem for a new class of interacting
Markov chain Monte Carlo algorithms. These stochastic algorithms have been
recently introduced to solve non-linear measure-valued equations. We provide
an original theoretical analysis based on semigroup techniques on
distribution spaces and fluctuation theorems for self-interacting random
fields. Additionally we also present a series of sharp mean error bounds in
terms of the semigroup associated with the first order expansion of the
limiting measure-valued process. We illustrate our results in the context of
Feynman-Kac semigroups
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Full text: PDF
Pages: 2130-2155
Published on: October 4, 2009
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Bibliography
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Electronic Journal of Probability. ISSN: 1083-6489 |
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