A general law of complete moment convergence for self-normalized sums.
Zang, Qing-Pei (2010)
Journal of Inequalities and Applications [electronic only]
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Zang, Qing-Pei (2010)
Journal of Inequalities and Applications [electronic only]
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Jamal Najim (2005)
ESAIM: Probability and Statistics
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A Large Deviation Principle (LDP) is proved for the family where the deterministic probability measure converges weakly to a probability measure and are -valued independent random variables whose distribution depends on and satisfies the following exponential moments condition: In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...
Zhao, Yuexu (2007)
Discrete Dynamics in Nature and Society
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Zang, Qing-Pei (2009)
Journal of Inequalities and Applications [electronic only]
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Li, Jie (2011)
Journal of Inequalities and Applications [electronic only]
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Deng, Dianliang (2009)
International Journal of Mathematics and Mathematical Sciences
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Zakhar Kabluchko, Axel Munk (2009)
ESAIM: Probability and Statistics
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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...
Gonchigdanzan, Khurelbaatar (2002)
International Journal of Mathematics and Mathematical Sciences
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Khurelbaatar Gonchigdanzan (2010)
ESAIM: Probability and Statistics
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We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.
Pak, Igor (1999)
Electronic Journal of Probability [electronic only]
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Gérard Ben Arous, Ofer Zeitouni (1998)
ESAIM: Probability and Statistics
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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.