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June, 1973 Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary Increments
C. C. Heyde, D. J. Scott
Ann. Probab. 1(3): 428-436 (June, 1973). DOI: 10.1214/aop/1176996937

Abstract

The main result in this paper is an invariance principle for the law of the iterated logarithm for square integrable martingales subject to fairly mild regularity conditions on the increments. When specialized to the case of identically distributed increments the result contains that of Stout [16] as well as the invariance principle for independent random variables of Strassen [17]. The martingale result is also used to obtain an invariance principle for the iterated logarithm law for a wide class of stationary ergodic sequences and a corollary is given which extends recent results of Oodaira and Yoshihara [10] on $\phi$-mixing processes.

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C. C. Heyde. D. J. Scott. "Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary Increments." Ann. Probab. 1 (3) 428 - 436, June, 1973. https://doi.org/10.1214/aop/1176996937

Information

Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0259.60021
MathSciNet: MR353403
Digital Object Identifier: 10.1214/aop/1176996937

Subjects:
Primary: 60B10
Secondary: 60F15 , 60G10 , 60G45

Keywords: $\Phi$-mixing , Invariance principles , iterated logarithm law , Martingales , stationary ergodic processes

Rights: Copyright © 1973 Institute of Mathematical Statistics

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