ESAIM: Probability and Statistics
- ESAIM: Probability and Statistics November 2005 9 : pp 19-37
- © EDP Sciences, SMAI, 2005
- DOI: 10.1051/ps:2005002 (About DOI)
- Published online by Cambridge University Press: 16 March 2011
Research Article
On the bounded laws of iterated logarithm in Banach space
Deng, Dianliang
Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4S 0A2 Canada; deng@math.uregina.ca
Abstract
In the present paper, by using the inequality due to Talagrand's isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.
(Received March 26 2004)
(Online publication November 15 2005)
Key Words:
- Banach space;
- bounded law of iterated logarithm;
- isoperimetric inequality;
- rademacher series;
- self-normalizer.
Mathematics Subject Classification:
- 60F05;
- 60B12;
- 60F99
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