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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

The sub-Gaussian norm of a binary random variable


Authors: V. V. Buldygin and K. K. Moskvichova
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 33-49
MSC (2010): Primary 60G50, 65B10, 60G15; Secondary 40A05
Published electronically: August 20, 2013
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Abstract: The exact values of the sub-Gaussian norms of Bernoulli random variables and binary random variables are found. Exponential bounds for the distributions of sums of centered binary random variables are studied for both cases of independent and dependent random variables. These bounds improve some known results.


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Additional Information

V. V. Buldygin
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: matan@kpi.ua

K. K. Moskvichova
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: matan@kpi.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00887-4
PII: S 0094-9000(2013)00887-4
Keywords: Sub-Gaussian random variable, sub-Gaussian norm, exponential inequalities, sums of random variables, Bernstein inequality, Hoeffding inequality
Received by editor(s): October 10, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society