inria-00227534, version 5
A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models
Bernard Bercu
1, 2Pierre Del Moral
1, 3Arnaud Doucet a, 4, 5
Electronic Journal of Probability 14, 73 (2009) 2130-2155
Résumé : 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.
- a – University of British Columbia
- 1 : Institut de Mathématiques de Bordeaux (IMB)
- CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
- 2 : CQFD (INRIA Bordeaux - Sud-Ouest)
- INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251
- 3 : ALEA (INRIA Bordeaux - Sud-Ouest)
- INRIA – Université de Bordeaux – CNRS : UMR5251
- 4 : Dept of Statistics & Dept of Computer Science
- University of British Columbia
- 5 : Department of Statistics (Statistics)
- University of British Columbia
- Domaine : Mathématiques/Probabilités
- Mots-clés : Multivariate and functional central limit theorems – random fields – martingale limit theorems – self-interacting Markov chains – Markov chain Monte Carlo models – and Feynman-Kac integrals.
- Référence interne : RR-6436
- Versions disponibles : v1 (31-01-2008) v2 (02-02-2008) v3 (04-02-2008) v4 (05-02-2008) v5 (18-06-2009)
- inria-00227534, version 5
- http://hal.inria.fr/inria-00227534
- oai:hal.inria.fr:inria-00227534
- Contributeur : Pierre Del Moral
- Soumis le : Jeudi 18 Juin 2009, 08:45:28
- Dernière modification le : Mercredi 17 Novembre 2010, 17:32:32
Documents associés
Exporter