Fluctuations of interacting Markov chain Monte Carlo methods |
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| Authors: | Bernard Bercu Pierre Del Moral Arnaud Doucet |
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| Affiliation: | 1. Centre INRIA Bordeaux Sud-Ouest & Institut de Mathématiques de Bordeaux, Université Bordeaux, 351 cours de la Libération 33405 Talence cedex, France;2. Applied Mathematics Center, Polytechnique, Route de Saclay, 9112 Palaiseau, France;3. Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, United Kingdom |
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| 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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| Keywords: | primary, 47H20, 60G35, 60J85, 62G09 secondary, 47D08, 47G10, 62L20 |
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