Abstract
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
Citation
Bernard Bercu. Pierre Del Moral. Arnaud Doucet. "A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Methods." Electron. J. Probab. 14 2130 - 2155, 2009. https://doi.org/10.1214/EJP.v14-701
Information