Bercu, Bernard; Del Moral, Pierre; Doucet, Arnaud A functional central limit theorem for a class of interacting Markov chain Monte Carlo methods. (English) Zbl 1191.60038 Electron. J. Probab. 14, 2130-2155 (2009). 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 Cited in 4 Documents MSC: 60F17 Functional limit theorems; invariance principles 60F05 Central limit and other weak theorems 68U20 Simulation (MSC2010) 60J22 Computational methods in Markov chains Keywords:multivariate and functional central limit theorems; random fields; martingale limit theorems; self-interacting Markov chains; Markov chain Monte Carlo methods; Feynman-Kac semigroups PDFBibTeX XMLCite \textit{B. Bercu} et al., Electron. J. Probab. 14, 2130--2155 (2009; Zbl 1191.60038) Full Text: DOI EuDML EMIS