Asymptotic expansions for the laplace approximations of sums of banach space-valued random variables

Sergio Albeverio, Song Liang

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let X i, i ∈ N, 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 Z n = E(exp(nφ(∑ i=1 n X 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 → ∞ is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.

Original languageEnglish
Pages (from-to)300-336
Number of pages37
JournalAnnals of Probability
Volume33
Issue number1
DOIs
Publication statusPublished - 2005 Jan
Externally publishedYes

Keywords

  • Asymptotic expansions
  • Banach space-valued random variables
  • i.i.d. Random vectors
  • Laplace approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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