A pair of complementary theorems on convergence rates in the law of large numbers-Reference-Cited by-同舟云学术

A pair of complementary theorems on convergence rates in the law of large numbers

Published:1967-01 Issue:1 Volume:63 Page:73-82
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Heyde C. C.,Rohatgi V. K.

Abstract

Introduction. Let Xi (i= 1, 2, 3,…) be a sequence of independent and identically distributed random variables with law ℒ(X) and write The Kolmogorov-Marcinkiewicz strong law of large numbers (Loève(6), p. 243) has the following statement:If E|X|r < ∞, then with cr = 0 or EX according as r 1 or r ≥ 1.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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