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November, 1983 Probability Estimates for the Small Deviations of $d$-Dimensional Random Walk
Philip S. Griffin
Ann. Probab. 11(4): 939-952 (November, 1983). DOI: 10.1214/aop/1176993443


Let $X_1, X_2, \cdots$ be a sequence of independent, identically distributed random variables taking values in $\mathbb{R}^d$ and $S_n = X_1 + \cdots + X_n$. For a large class of distributions we obtain estimates for the probability that $S_n$ is in a ball centered at the origin. Such an estimate would follow from a local limit theorem if $X_1$ were in the domain of attraction of a stable law.


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Philip S. Griffin. "Probability Estimates for the Small Deviations of $d$-Dimensional Random Walk." Ann. Probab. 11 (4) 939 - 952, November, 1983.


Published: November, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0519.60044
MathSciNet: MR714957
Digital Object Identifier: 10.1214/aop/1176993443

Primary: 60G50
Secondary: 60E15

Keywords: local limit theorem , Probability estimate

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 4 • November, 1983
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