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Laplace approximations for sums of independent random vectors
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  • Published: February 2000

Laplace approximations for sums of independent random vectors

  • Shigeo Kusuoka1 &
  • Song Liang1 

Probability Theory and Related Fields volume 116, pages 221–238 (2000)Cite this article

  • 88 Accesses

  • 5 Citations

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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.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Meguro, Tokyo, 153 Japan, , , , , , JP

    Shigeo Kusuoka & Song Liang

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  1. Shigeo Kusuoka
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  2. Song Liang
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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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  • Issue Date: February 2000

  • DOI: https://doi.org/10.1007/PL00008727

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  • Mathematics Subject Classification (1991): 60F10, 60B12
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