A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
DOUCET, Arnaud
Dept of Statistics & Dept of Computer Science
Department of Statistics [Vancouver] [UBC Statistics]
Dept of Statistics & Dept of Computer Science
Department of Statistics [Vancouver] [UBC Statistics]
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
DOUCET, Arnaud
Dept of Statistics & Dept of Computer Science
Department of Statistics [Vancouver] [UBC Statistics]
< Reduce
Dept of Statistics & Dept of Computer Science
Department of Statistics [Vancouver] [UBC Statistics]
Language
en
Article de revue
This item was published in
Electronic Journal of Probability. 2009, vol. 14, n° 73, p. 2130-2155
Institute of Mathematical Statistics (IMS)
English Abstract
We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original stochastic analysis based on ...Read more >
We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original stochastic analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interaction random fields. Besides the fluctuation analysis of these models, we also present a series of sharp $\LL_m$-mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure valued process, yielding what seems to be the first results of this type for this class of interacting processes. We illustrate these results in the context of Feynman-Kac integration semigroups arising in physics, biology and stochastic engineering science.Read less <
English Keywords
and Feynman-Kac integrals
Multivariate and functional central limit theorems
random fields
martingale limit theorems
self-interacting Markov chains
Markov chain Monte Carlo models
and Feynman-Kac integrals.
Origin
Hal imported