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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Ordinal law of the iterated logarithm in Banach lattices and some applications


Author: I. K. Matsak
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 77-91
MSC (2000): Primary 60B12
Published electronically: June 29, 2007
MathSciNet review: 2336780
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Abstract: Necessary and sufficient conditions are found for the ordinal law of the iterated logarithm in Banach lattices of type $ L^p$. As a corollary of our general results, we obtain a new law of the iterated logarithm for empirical processes in the spaces $ L^p(-\infty,\infty)$.


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Additional Information

I. K. Matsak
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Glushkov Avenue, 6, Kyiv, 03127, Ukraine
Address at time of publication: Kyiv National University for Technology and Design, Nemyrovych-Danchenko Street, 2, 01601, GSP, Kyiv, Ukraine
Email: m_i_k@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00699-0
PII: S 0094-9000(07)00699-0
Keywords: Law of the iterated logarithm, Banach lattices, empirical processes
Received by editor(s): May 7, 2004
Published electronically: June 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society