The Annals of Probability

Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms

Luisa Turrin Fernholz and Henry Teicher

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Abstract

Strong laws of large numbers, obtained for positive, independent random variables, are utilized to prove iterated logarithm laws (with a nonrandom normalizing sequence) for a class of martingales. A law of the iterated logarithm is also established for certain random quadratic forms.

Article information

Source
Ann. Probab., Volume 8, Number 4 (1980), 765-774.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994664

Digital Object Identifier
doi:10.1214/aop/1176994664

Mathematical Reviews number (MathSciNet)
MR577314

Zentralblatt MATH identifier
0442.60032

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems

Keywords
Strong law of large numbers stability law of the iterated logarithm $U$-statistics random quadratic forms

Citation

Fernholz, Luisa Turrin; Teicher, Henry. Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms. Ann. Probab. 8 (1980), no. 4, 765--774. doi:10.1214/aop/1176994664. https://projecteuclid.org/euclid.aop/1176994664


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