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Teoriya Veroyatnostei i ee Primeneniya, 2000, Volume 45, Issue 1, Pages 194–202
DOI: https://doi.org/10.4213/tvp338 (Mi tvp338) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

On probablity and moment inequalties for dependent random variables

S. V. Nagaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (452 kB) Citations (6)
DOI: https://doi.org/10.4213/tvp338
Abstract: The paper obtains the upper estimate for the probability that a norm of a sum of dependent random variables with values in the Banach space exceeds a given level. This estimate is principally different from the probability inequalities for sums of dependent random variables known up to now both by form and method of proof. It contains only one of the countable number of mixing coefficients. Due to the introduction of a quantile the estimate does not contain moments. The constants in the estimate are calculated explicitly. As in the case of independent summands, the moment inequalities are derived with the help of the estimate obtained.
Keywords: Banach space, Gaussian random vector, Hilbert space, quantile, uniform mixing coefficient, Hoffman–Jorgensen inequality, Marcinkiewicz–Zygmund inequality, Euler function.
Received: 10.03.1998
English version:
Theory of Probability and its Applications, 2000, Volume 45, Issue 1, Pages 152–160
DOI: https://doi.org/10.1137/S0040585X97978142
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Nagaev, “On probablity and moment inequalties for dependent random variables”, Teor. Veroyatnost. i Primenen., 45:1 (2000), 194–202; Theory Probab. Appl., 45:1 (2000), 152–160
Citation in format AMSBIB
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\paper On probablity and moment inequalties for dependent random variables
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\pages 194--202
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\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 45
\issue 1
\pages 152--160
\crossref{https://doi.org/10.1137/S0040585X97978142}
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  • https://doi.org/10.4213/tvp338
  • https://www.mathnet.ru/eng/tvp/v45/i1/p194
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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