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Laplace approximations for sums of independent random vectors


Bolthausen, E (1986). Laplace approximations for sums of independent random vectors. Probability Theory and Related Fields, 72(2):305-318.

Abstract

Let X i , i∈ℕ, be i.i.d. B-valued random variables where B is a real separable Banach space, and Φ a mapping B→ℝ. Under some conditions an asymptotic evaluation of Z n =E(exp(nΦ(∑ i=1 n X i /n))) is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums ∑ i=1 n X i under the law transformed by the density exp(nΦ (∑ i=1 n X i /n))/Z n.

Abstract

Let X i , i∈ℕ, be i.i.d. B-valued random variables where B is a real separable Banach space, and Φ a mapping B→ℝ. Under some conditions an asymptotic evaluation of Z n =E(exp(nΦ(∑ i=1 n X i /n))) is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums ∑ i=1 n X i under the law transformed by the density exp(nΦ (∑ i=1 n X i /n))/Z n.

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38 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Laplace approximations; Banach space; asymptotic evaluation
Language:English
Date:1986
Deposited On:20 Oct 2009 11:10
Last Modified:05 Apr 2016 13:29
Publisher:Springer
ISSN:0178-8051
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/BF00699109

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