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2009 A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods
Bernard Bercu, Pierre Del Moral, Arnaud Doucet
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Electron. J. Probab. 14: 2130-2155 (2009). DOI: 10.1214/EJP.v14-701

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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Bernard Bercu. Pierre Del Moral. Arnaud Doucet. "A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods." Electron. J. Probab. 14 2130 - 2155, 2009. https://doi.org/10.1214/EJP.v14-701

Information

Accepted: 4 October 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60038
MathSciNet: MR2550295
Digital Object Identifier: 10.1214/EJP.v14-701

Subjects:
Primary: 60F05
Secondary: 60J05 , 60J20 , 68U20 , 80M31

Keywords: Feynman-Kac semigroups , Markov chain Monte Carlo methods , martingale limit theorems , Multivariate and functional central limit theorems , Random fields , self-interacting Markov chains

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