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June, 1978 Marcinkiewicz Laws and Convergence Rates in the Law of Large Numbers for Random Variables with Multidimensional Indices
Allan Gut
Ann. Probab. 6(3): 469-482 (June, 1978). DOI: 10.1214/aop/1176995531

Abstract

Consider a set of independent identically distributed random variables indexed by $Z^d_+$, the positive integer $d$-dimensional lattice points, $d \geqq 2$. The classical Kolmogorov-Marcinkiewicz strong law of large numbers is generalized to this case. Also, convergence rates in the law of large numbers are derived, i.e., the rate of convergence to zero of, for example, the tail probabilities of the sample sums is determined.

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Allan Gut. "Marcinkiewicz Laws and Convergence Rates in the Law of Large Numbers for Random Variables with Multidimensional Indices." Ann. Probab. 6 (3) 469 - 482, June, 1978. https://doi.org/10.1214/aop/1176995531

Information

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

zbMATH: 0383.60030
MathSciNet: MR494431
Digital Object Identifier: 10.1214/aop/1176995531

Subjects:
Primary: 60F15
Secondary: 60G50

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 3 • June, 1978
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