Laplace approximations for sums of independent random vectors
作者:Shigeo Kusuoka、Song Liang
DOI:10.1007/pl00008727
日期:2000.2
Let X-i, i is an element of N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Phi be a mapping B --> R. Under a central limit theorem assumption, an asymptotic evaluation of Z(n) = E (exp (n Phi (Sigma(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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