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A remark on the central limit question for dependent random variables

Published online by Cambridge University Press:  14 July 2016

Richard C. Bradley Jr
Richard C. Bradley Jr*
Affiliation:
Columbia University
*
∗Postal address: Department of Mathematical Statistics, Columbia University, New York, NY 10027, U.S.A.
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Abstract

Given a strictly stationary sequence {Xk, k = …, −1,0,1, …} of r.v.'s one defines for n = 1, 2, 3 …, . Here an example of {Xk} is given with finite second moments, for which Var(X1 + … + Xn)→∞ and ρ n → 0 as n→∞, but (X1 + … + Xn) fails to be asymptotically normal; instead there is partial attraction to non-stable limit laws.

Keywords

STRICTLY STATIONARYMIXING CONDITIONMAXIMAL CORRELATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 94 - 101
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research partially supported by the National Science Foundation and the Office of Naval Research.

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