On the limiting behavior of tail series

DOI10.1016/j.jspi.2006.06.017zbMath1108.60024OpenAlexW2043560660MaRDI QIDQ866639

Andrew Rosalsky

Publication date: 14 February 2007

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2006.06.017

zbMATH Keywords

rate of convergencestrong law of large numberssequence of independent random variablesalmost certainly convergent series of random variables

Mathematics Subject Classification ID

Strong limit theorems (60F15)

Cites Work

• Almost sure behavior of tail series in functional spaces
• A strong invariance theorem for the strong law of large numbers
• The speed of convergence of a martingale
• Rates of convergence for tail series
• An application of the Ryll-Nardzewski-Woyczyński theorem to a uniform weak law for tail series of weighted sums of random elements in Banach spaces
• Wittmann's law of iterated logarithm for tail sums of \(B\)-valued random variables
• Iterated logarithm laws with random subsequences
• Iterated Logarithm laws for weighted averages
• On central limit and iterated logarithm supplements to the martingale convergence theorem
• On convergence of series of independent random elements in banach spaces
• On the Limiting Behavior of a Random Walk
• On the rate of convergence of series of banach space valued random elements
• On convergence of series of random variables with applications to martingale convergence and to convergence of series with orthogonal summands
• A Note on the Weak Law of Large Numbers
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