Fluctuations of Interacting Markov Chain Monte Carlo Methods

Details Fluctuations of Interacting Markov Chain Monte Carlo Methods Fluctuations of Interacting Markov Chain Monte Carlo Methods

2012-01-02

arxiv.org/abs/1201.0480v1

Mathematics

Probability

Second revision of the INRIA-RR-6438 technical report (available February 2008) at http://hal.inria.fr/docs/00/23/92/48/PDF/RR

Scientific paper

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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