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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the central limit theorem for square-integrable processes
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by Marjorie G. Hahn PDF
Proc. Amer. Math. Soc. 64 (1977), 331-334 Request permission

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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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