Laplace approximations for sums of independent random vectors

Shigeo Kusuoka, Song Liang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B → R. Under a central limit theorem assumption, an asymptotic evaluation of Zn = E (exp (nΦ(Σni=1 Xi/n))), up to a factor (1 + 0(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption.

Original languageEnglish
Pages (from-to)221-238
Number of pages18
JournalProbability Theory and Related Fields
Volume116
Issue number2
DOIs
Publication statusPublished - 2000 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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