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 Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 1, Pages 194–202 (Mi tvp338)

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

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.

DOI: https://doi.org/10.4213/tvp338

Full text: PDF file (452 kB)

English version:
Theory of Probability and its Applications, 2000, 45:1, 152–160

Bibliographic databases:

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
\Bibitem{Nag00} \by S.~V.~Nagaev \paper On probablity and moment inequalties for dependent random variables \jour Teor. Veroyatnost. i Primenen. \yr 2000 \vol 45 \issue 1 \pages 194--202 \mathnet{http://mi.mathnet.ru/tvp338} \crossref{https://doi.org/10.4213/tvp338} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1810984} \zmath{https://zbmath.org/?q=an:0981.60005} \transl \jour Theory Probab. Appl. \yr 2000 \vol 45 \issue 1 \pages 152--160 \crossref{https://doi.org/10.1137/S0040585X97978142} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000167428900011} 

• http://mi.mathnet.ru/eng/tvp338
• https://doi.org/10.4213/tvp338
• http://mi.mathnet.ru/eng/tvp/v45/i1/p194

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Nagaev, V. I. Chebotarev, “On the Accuracy of Gaussian Approximation in Hilbert Space”, Siberian Adv. Math., 15:1 (2005), 11–73
2. Theory Probab. Appl., 49:2 (2005), 311–323
3. S. V. Nagaev, “On probability and moment inequalities for supermartingales and martingales”, Theory Probab. Appl., 51:2 (2007), 367–377
4. Szewczak Z.S., “On Limit Theorems for Continued Fractions”, Journal of Theoretical Probability, 22:1 (2009), 239–255
5. Szewczak Z.S., “Marcinkiewicz laws with infinite moments”, Acta Mathematica Hungarica, 127:1–2 (2010), 64–84
6. Szewczak Z.S., “On Marcinkiewicz-Zygmund laws”, J Math Anal Appl, 375:2 (2011), 738–744
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