Fluctuations of interacting Markov chain Monte Carlo methods

Bernard Bercu, Pierre Del Moral and Arnaud Doucet

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1304-1331

Abstract: We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators and semigroup techniques to analyze the fluctuations of their occupation measures around their limiting values.

Keywords: Multivariate central limit theorems; Random fields; Martingale limit theorems; Self-interacting Markov chains; Markov chain Monte Carlo algorithms (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:4:p:1304-1331

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DOI: 10.1016/j.spa.2012.01.001

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