Sample behavior and laws of large numbers for Gaussian random elements.
Ergemlidze, Z., Shangua, A., Tarieladze, V. (2003)
Georgian Mathematical Journal
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Ergemlidze, Z., Shangua, A., Tarieladze, V. (2003)
Georgian Mathematical Journal
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Mamporia, B. (2000)
Georgian Mathematical Journal
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Seleši, Dora (2007)
Novi Sad Journal of Mathematics
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Mittmann, Katrin, Steinwart, Ingo (2003)
Georgian Mathematical Journal
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Matsak, Ivan, Plichko, Anatolij (2002)
Georgian Mathematical Journal
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Chobanyan, S., Salehi, H. (2001)
Georgian Mathematical Journal
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Buldygin, V.V., Koval, V.A. (2001)
Georgian Mathematical Journal
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Nguyen Van Huan, Nguyen Van Quang (2012)
Kybernetika
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We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
Fleischmann, Klaus, Mörters, Peter, Wachtel, Vitali (2006)
Electronic Journal of Probability [electronic only]
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Lotov, V.I. (2002)
Sibirskij Matematicheskij Zhurnal
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Kvaratskhelia, V. (2000)
Georgian Mathematical Journal
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Marian Jabłoński
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Let be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let be a sequence of elements of with . It is shown that the distribution oftends to the normal distribution N(0,1) as n → ∞. 1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.