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.
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Received: 19 September 1997 / Revised version:22 April 1999
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Kusuoka, S., Liang, S. Laplace approximations for sums of independent random vectors. Probab Theory Relat Fields 116, 221–238 (2000). https://doi.org/10.1007/PL00008727
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DOI: https://doi.org/10.1007/PL00008727