A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | BERCU, Bernard | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Advanced Learning Evolutionary Algorithms [ALEA] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Dept of Statistics & Dept of Computer Science | |
| hal.structure.identifier | Department of Statistics [Vancouver] [UBC Statistics] | |
| dc.contributor.author | DOUCET, Arnaud | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 1083-6489 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Mathematical Statistics (IMS) | |
| dc.subject.en | and Feynman-Kac integrals | |
| dc.subject.en | Multivariate and functional central limit theorems | |
| dc.subject.en | random fields | |
| dc.subject.en | martingale limit theorems | |
| dc.subject.en | self-interacting Markov chains | |
| dc.subject.en | Markov chain Monte Carlo models | |
| dc.subject.en | and Feynman-Kac integrals. | |
| dc.title.en | A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.journal | Electronic Journal of Probability | |
| bordeaux.page | 2130-2155 | |
| bordeaux.volume | 14 | |
| bordeaux.issue | 73 | |
| bordeaux.peerReviewed | oui | |
| bordeaux.type.report | rr | |
| hal.identifier | inria-00227534 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00227534v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Electronic%20Journal%20of%20Probability&rft.date=2009&rft.volume=14&rft.issue=73&rft.spage=2130-2155&rft.epage=2130-2155&rft.eissn=1083-6489&rft.issn=1083-6489&rft.au=BERCU,%20Bernard&DEL%20MORAL,%20Pierre&DOUCET,%20Arnaud&rft.genre=article |
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