Electronic Journal of Probability

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods

Bernard Bercu, Pierre Del Moral, and Arnaud Doucet

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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

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 73, 2130-2155.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60J05: Discrete-time Markov processes on general state spaces 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 68U20: Simulation [See also 65Cxx] 80M31: Monte Carlo methods

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

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Bercu, Bernard; Del Moral, Pierre; Doucet, Arnaud. A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods. Electron. J. Probab. 14 (2009), paper no. 73, 2130--2155. doi:10.1214/EJP.v14-701. https://projecteuclid.org/euclid.ejp/1464819534

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