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December, 1975 On Convergence in $r$-Mean of Normalized Partial Sums
S. W. Dharmadhikari, M. Sreehari
Ann. Probab. 3(6): 1023-1024 (December, 1975). DOI: 10.1214/aop/1176996228

Abstract

Suppose $S_n = \sum^n_1 X_j$, where $\{X_n\}$ is a sequence of random variables. Under progressively weaker hypotheses, Pyke and Root (1968), Chatterji (1969) and Chow (1971) have proved that $E|S_n - b_n|^r = o(n)$, where $0 < r < 2$ and $\{b_n\}$ is properly chosen. This paper gives a fairly elementary proof of Chow's result under further weakened hypotheses.

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S. W. Dharmadhikari. M. Sreehari. "On Convergence in $r$-Mean of Normalized Partial Sums." Ann. Probab. 3 (6) 1023 - 1024, December, 1975. https://doi.org/10.1214/aop/1176996228

Information

Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0348.60036
MathSciNet: MR397869
Digital Object Identifier: 10.1214/aop/1176996228

Subjects:
Primary: 60F15
Secondary: 60G45

Keywords: $r$-mean convergence , Martingales

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • December, 1975
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