BÉRARD, Jean; DEL MORAL, Pierre; DOUCET, Arnaud

doi:10.1214/EJP.v19-3428

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BÉRARD, Jean
Institut de Recherche Mathématique Avancée [IRMA]
Institut Camille Jordan [ICJ]

DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]

DOUCET, Arnaud
Department of Statistics [Oxford]

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Electronic Journal of Probability. 2014, vol. 19

Institute of Mathematical Statistics (IMS)

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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.< Leer menos

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A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants

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