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October, 1978 Convergence Rates of Large Deviation Probabilities in the Multidimensional Case
Josef Steinebach
Ann. Probab. 6(5): 751-759 (October, 1978). DOI: 10.1214/aop/1176995426

Abstract

Let $\{W_n\}_{n=1,2,\cdots}$ denote a sequence of $k$-dimensional random vectors on a probability space $(\Omega, \mathscr{A}, P)$. Using moment-generating function techniques sufficient conditions are given for the existence of limits $\rho(A) = \lim_{n\rightarrow\infty} \lbrack P(W_n \not\in k_n A)\rbrack^{1/k_n}$ for certain subsets $A \subset R^k$, where $\{k_n\}_{n=1,2,\cdots}$ is a divergent sequence of positive real numbers. The results are multivariate analogs of well-known large deviation theorems on the real line.

Citation

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Josef Steinebach. "Convergence Rates of Large Deviation Probabilities in the Multidimensional Case." Ann. Probab. 6 (5) 751 - 759, October, 1978. https://doi.org/10.1214/aop/1176995426

Information

Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0396.60032
MathSciNet: MR501289
Digital Object Identifier: 10.1214/aop/1176995426

Subjects:
Primary: 60F10

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • October, 1978
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