Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables

dc.creatorAlbeverio, Sergio
dc.creatorLiang, Song
dc.date2005-03-25
dc.date.accessioned2026-07-07T05:18:30Z
dc.date.available2026-07-07T05:18:30Z
dc.descriptionLet X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φbe a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (nΦ(\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n as n\to \infty is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000001017 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503601
dc.identifierhttp://arxiv.org/abs/math/0503601
dc.identifierAnnals of Probability 2005, Vol. 33, No. 1, 300-336
dc.identifierdoi:10.1214/009117904000001017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74680
dc.subjectProbability
dc.subject62E20, 60F10, 60B12. (Primary)
dc.titleAsymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables
dc.typetext

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