# 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Laplace approximations; Banach space; asymptotic evaluation English 1986 20 Oct 2009 11:10 05 Apr 2016 13:29 Springer 0178-8051 The original publication is available at www.springerlink.com https://doi.org/10.1007/BF00699109