A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants
| hal.structure.identifier | Institut de Recherche Mathématique Avancée [IRMA] | |
| hal.structure.identifier | Institut Camille Jordan [ICJ] | |
| dc.contributor.author | BÉRARD, Jean | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Department of Statistics [Oxford] | |
| dc.contributor.author | DOUCET, Arnaud | |
| dc.date.accessioned | 2024-04-04T03:22:01Z | |
| dc.date.available | 2024-04-04T03:22:01Z | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 1083-6489 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194713 | |
| dc.description.abstractEn | This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central limit theorem for a fixed time horizon n as the number of particles N goes to infinity. Here, we study the situation where both n and N go to infinity in such a way that lim n→∞ . In this context, Pitt et al. \cite{pitt2012} recently conjectured that a lognormal central limit theorem should hold. We formally establish this result here, under general regularity assumptions on the model. We also discuss special classes of models (time-homogeneous environment and ergodic random environment) for which more explicit descriptions of the limiting bias and variance can be obtained. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Mathematical Statistics (IMS) | |
| dc.title.en | A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1214/EJP.v19-3428 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.journal | Electronic Journal of Probability | |
| bordeaux.volume | 19 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01019391 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01019391v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Electronic%20Journal%20of%20Probability&rft.date=2014&rft.volume=19&rft.eissn=1083-6489&rft.issn=1083-6489&rft.au=B%C3%89RARD,%20Jean&DEL%20MORAL,%20Pierre&DOUCET,%20Arnaud&rft.genre=article |
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