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

de Acosta, A.

doi:10.1090/S0002-9947-1992-1046015-4

Moderate deviations and associated Laplace approximations for sums of independent random vectors
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Trans. Amer. Math. Soc. 329 (1992), 357-375 Request permission

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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