Laplace approximations for sums of independent random vectors |
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Authors: | Shigeo Kusuoka Song Liang |
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Affiliation: | (1) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Meguro, Tokyo, 153 Japan, JP |
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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 mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z n = E (exp (n Φ (∑ i =1 n X i /n))), up to a factor (1 + o(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. Received: 19 September 1997 / Revised version:22 April 1999 |
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Keywords: | Mathematics Subject Classification (1991): 60F10 60B12 |
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