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June, 1972 Central Limit Theorems for Sums of Dependent Vector Variables
W. J. Cocke
Ann. Math. Statist. 43(3): 968-976 (June, 1972). DOI: 10.1214/aoms/1177692559


We prove the following central limit theorems for sums of mutually dependent random vector variables: Given that a sequence of random vector variables satisfies a certain type of decoupling condition (and two milder restrictions), we present a Lindeberg-Feller condition which we show to be both necessary and sufficient for central limit behavior. The decoupling condition and one of the two milder conditions is then applied to a Markov process with stationary transition mechanism.


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W. J. Cocke. "Central Limit Theorems for Sums of Dependent Vector Variables." Ann. Math. Statist. 43 (3) 968 - 976, June, 1972.


Published: June, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0244.60015
MathSciNet: MR301780
Digital Object Identifier: 10.1214/aoms/1177692559

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 3 • June, 1972
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