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Theory of Probability and Mathematical Statistics

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Convergence of series of Gaussian Markov sequences


Author: M. K. Runovska
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 149-162
MSC (2010): Primary 60G50, 65B10, 60G15; Secondary 40A05
DOI: https://doi.org/10.1090/S0094-9000-2012-00848-X
Published electronically: February 2, 2012
MathSciNet review: 2768855
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Abstract | References | Similar Articles | Additional Information

Abstract: We find necessary and sufficient conditions for the almost sure convergence of sums of centered Gaussian Markov sequences.


References [Enhancements On Off] (What's this?)

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  • 2. V. V. Buldygin and S. A. Solntsev, Functional methods in problems of the summation of random variables, Naukova Dumka, Kiev, 1989. (Russian) MR 1007589 (91i:60013)
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  • 5. N. N. Vorob'ev, Theory of Series, Nauka, Moscow, 1979. (Russian) MR 548875 (80i:40001)

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Additional Information

M. K. Runovska
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (“KPI”), Peremogy Avenue 37, Kyiv 03056, Ukraine
Email: matan@ntu-kpi.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2012-00848-X
Keywords: Gaussian Markov sequence of random variables, almost sure convergence of random series, theory of sums of independent random elements with operator normalizations
Received by editor(s): May 17, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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