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On the converse to the iterated logarithm law

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
University of Sheffield
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Extract

Let Xi, i = 1, 2, 3,… be a sequence of independent and identically distributed random variables with law ℓ(X) and write. if EX= 0 and EX2 =σ2 < ∞, the law of the iterated logarithm (Hartman and Wintner [1]) tells us that

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 210 - 215
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Hartman, P. and Wintner, A. (1941) On the law of the iterated logarithm. Amer. J. Math. 63, 169–176.Google Scholar
[2] Loève, M. (1963) Probability Theory. 3rd edition. Van Nostrand, New York.Google Scholar
[3] Stone, C. (1966) The growth of a recurrent random walk. Ann. Math. Statist. 37, 1040–1041.Google Scholar
[4] Strassen, V. (1966) A converse to the law of the iterated logarithm. Z. Wahrscheinlichkeitsth. 4, 265–268.Google Scholar