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Issue ESAIM: P&S Volume 9, 2005 Page(s) 19 - 37 DOI 10.1051/ps:2005002

ESAIM: P&S, February 2005, Vol. 9, pp. 19-37
DOI: 10.1051/ps:2005002

On the bounded laws of iterated logarithm in Banach space

Dianliang Deng

Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4S 0A2 Canada; deng@math.uregina.ca

(Received March 26, 2004. )

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.

Mathematics Subject Classification. 60F05, 60B12, 60F99.

Key words: Banach space, bounded law of iterated logarithm, isoperimetric inequality, rademacher series, self-normalizer.


© EDP Sciences, SMAI 2005

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