On Feller's criterion for the law of the iterated logarithm.
Li, Deli, Rao, M.Bhaskara, Wang, Xiangchen (1994)
International Journal of Mathematics and Mathematical Sciences
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Li, Deli, Rao, M.Bhaskara, Wang, Xiangchen (1994)
International Journal of Mathematics and Mathematical Sciences
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Mason, David M., Zinn, Joel (2005)
Electronic Communications in Probability [electronic only]
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Oliveira, P.E., Suquet, Ch. (1996)
Portugaliae Mathematica
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Zhao, Yuexu (2007)
Discrete Dynamics in Nature and Society
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Borisov, I.S. (2003)
International Journal of Mathematics and Mathematical Sciences
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Guang-hui Cai (2011)
Czechoslovak Mathematical Journal
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In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite th moment and the covariance coefficient exponentially decreases to . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
Járai, Antal A., Kesten, Harry (2004)
Electronic Communications in Probability [electronic only]
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Ladoucette, Sophie A., Teugels, Jef J. (2006)
Publications de l'Institut Mathématique. Nouvelle Série
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Cai, Guang-Hui (2006)
Discrete Dynamics in Nature and Society
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Dianliang Deng (2005)
ESAIM: Probability and Statistics
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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.