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.

Keywords: Banach space, bounded law of iterated logarithm, isoperimetric inequality, Rademacher series, self-normalizer

@article{PS_2005__9__19_0, author = {Deng, Dianliang}, title = {On the bounded laws of iterated logarithm in {Banach} space}, journal = {ESAIM: Probability and Statistics}, pages = {19--37}, publisher = {EDP-Sciences}, volume = {9}, year = {2005}, doi = {10.1051/ps:2005002}, mrnumber = {2148959}, zbl = {1136.60314}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2005002/} }

Deng, Dianliang. On the bounded laws of iterated logarithm in Banach space. ESAIM: Probability and Statistics, Volume 9 (2005), pp. 19-37. doi : 10.1051/ps:2005002. http://www.numdam.org/articles/10.1051/ps:2005002/

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