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A functional central limit theorem for a class of interacting Markov chain Monte Carlo methods. (English) Zbl 1191.60038

Summary: 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

MSC:

60F17 Functional limit theorems; invariance principles
60F05 Central limit and other weak theorems
68U20 Simulation (MSC2010)
60J22 Computational methods in Markov chains
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