Fluctuations of Interacting Markov Chain Monte Carlo Methods

2012/01/02 by Bernard Bercu, Pierre Del Moral, Bercu, Bernard +3
Mathematics · #47G10 #60G35 #60J85 #62G09 #62L20 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Primary: 47H20 #Probability (math.PR) #Secondary: 47D08 #Statistics Theory (math.ST) #math.PR #math.ST #msc:47D08 #msc:47G10 #msc:47H20 #msc:60G35 #msc:60J85 #msc:62G09 #msc:62L20 #stat.CO #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1201.0480

Second revision of the INRIA-RR-6438 technical report (available February 2008) at http://hal.inria.fr/docs/00/23/92/48/PDF/RR-6438.pdf To appear in Stochastic Processes and Their Applications

arxiv created 2012/01/02 · arxiv updated 2012/01/04

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.

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