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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
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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  • 3. Valery Buldygin and Serguei Solntsev, Asymptotic behaviour of linearly transformed sums of random variables, Mathematics and its Applications, vol. 416, Kluwer Academic Publishers Group, Dordrecht, 1997. Translated from the 1989 Russian original by Vladimir Zaiats and revised, updated and expanded by the authors. MR 1471203
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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

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