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Zap. Nauchn. Sem. POMI, 2013, Volume 420, Pages 127–141 (Mi znsl5730)  

On the strong law of large numbers for sequences of dependent random variables with finite second moments

V. M. Korchevsky

Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, Russia

Abstract: New sufficient conditions of a.s. convergence of the series $\sum_{n=1}^\infty X_n$ and new sufficient conditions for the applicability of the strong law of large numbers are established for a sequence of dependent random variables $\{X_n\}_{n=1}^\infty$ with finite second moments. These results are generalizations of the well known theorems on a.s. convergence of the series of orthogonal random variables and on the strong law of large numbers for orthogonal random variables (Men'shov–Rademacher and Petrov's theorems). It is shown that some of the results obtained are optimal.

Key words and phrases: strong law of large numbers, sequences of dependent random variables, almost sure convergence of series, orthogonal random variables.

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English version:
Journal of Mathematical Sciences (New York), 2015, 206:2, 197–206

UDC: 519.214
Received: 28.10.2013

Citation: V. M. Korchevsky, “On the strong law of large numbers for sequences of dependent random variables with finite second moments”, Probability and statistics. Part 20, Zap. Nauchn. Sem. POMI, 420, POMI, St. Petersburg, 2013, 127–141; J. Math. Sci. (N. Y.), 206:2 (2015), 197–206

Citation in format AMSBIB
\Bibitem{Kor13}
\by V.~M.~Korchevsky
\paper On the strong law of large numbers for sequences of dependent random variables with finite second moments
\inbook Probability and statistics. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 420
\pages 127--141
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5730}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 206
\issue 2
\pages 197--206
\crossref{https://doi.org/10.1007/s10958-015-2303-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953349834}


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