Ordinal law of the iterated logarithm in Banach lattices and some applications
Author:
I. K. Matsak
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 74 (2007), 77-91
MSC (2000):
Primary 60B12
DOI:
https://doi.org/10.1090/S0094-9000-07-00699-0
Published electronically:
June 29, 2007
MathSciNet review:
2336780
Full-text PDF Free Access
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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 $L^p(-\infty ,\infty )$.
References
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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
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
