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January 2005 Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables
Sergio Albeverio, Song Liang
Ann. Probab. 33(1): 300-336 (January 2005). DOI: 10.1214/009117904000001017

Abstract

Let Xi, iN, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a smooth enough mapping from B into R. An asymptotic evaluation of Zn=E(exp(nΦ(∑i=1nXi/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 Zn as n→∞ is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.

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Sergio Albeverio. Song Liang. "Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables." Ann. Probab. 33 (1) 300 - 336, January 2005. https://doi.org/10.1214/009117904000001017

Information

Published: January 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1092.62024
MathSciNet: MR2118867
Digital Object Identifier: 10.1214/009117904000001017

Subjects:
Primary: 60B12 , 60F10 , 62E20

Keywords: asymptotic expansions , Banach space-valued random variables , i.i.d. random vectors , Laplace approximation

Rights: Copyright © 2005 Institute of Mathematical Statistics

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