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A converse to the log-log law for Martingales

Published online by Cambridge University Press:  09 April 2009

W. L. Steiger
W. L. Steiger
Affiliation:
Centre de Recherches Mathématiques, Université de Montréal, Canada
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For sums of independent and identically distributed random variables xn, the HartmanWintner law of the iterated logarithm is equivalent to xn ∈ L2. We show that this is also true when the xn, form a stationary, ergodic martingale difference sequence. This is accomplished by extending a theorem of Volker Strassen to the present context.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 496 - 499
Copyright
Copyright © Australian Mathematical Society 1974

References

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