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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Moderate deviations and associated Laplace approximations for sums of independent random vectors


Author: A. de Acosta
Journal: Trans. Amer. Math. Soc. 329 (1992), 357-375
MSC: Primary 60F10; Secondary 60B12
DOI: https://doi.org/10.1090/S0002-9947-1992-1046015-4
MathSciNet review: 1046015
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Abstract: Let $ \{ {X_j}\} $ be an i.i.d. sequence of Banach space valued r.v.'s and let $ {S_n} = \sum\nolimits_{j = 1}^n {{X_j}} $. For certain positive sequences $ {b_n} \to \infty $, we determine the exact asymptotic behavior of $ E{\operatorname{exp}}\{ (b_n^2/n)\Phi ({S_n}/{b_n})\} $, where $ \Phi $ is a smooth function. We also prove a large deviation principle for $ \{ \mathcal{L}({S_n}/{b_n})\} $.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1046015-4
Keywords: Moderate and large deviations, exact asymptotics, Laplace approximation
Article copyright: © Copyright 1992 American Mathematical Society

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