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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the central limit theorem for square-integrable processes


Author: Marjorie G. Hahn
Journal: Proc. Amer. Math. Soc. 64 (1977), 331-334
MSC: Primary 60F05
DOI: https://doi.org/10.1090/S0002-9939-1977-0448487-X
MathSciNet review: 0448487
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Abstract: A method is given for constructing sample-continuous processes which do not satisfy the central limit theorem in $C[0,1]$. Let $\{ X(t):t \in [0,1]\}$ be a stochastic process. Using our method we characterize all possible nonnegative functions f for which the condition \[ E( X(t) - X(s) )^2 \leqslant f( | t - s | )\] alone is sufficient to imply that $X(t)$ satisfies the central limit theorem in $C[0,1]$.


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Keywords: Central limit theorem, second-order processes, random Fourier series
Article copyright: © Copyright 1977 American Mathematical Society