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.

**1.**V. V. Buldygin,*The strong law of large numbers and the convergence to zero of Gaussian sequences*, Teor. Verojatnost. i Mat. Statist.**19**(1978), 33-41; English transl. in Theor. Probability Math. Statist.**19**(1980), 35-43. MR**0494429 (58:13294)****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)****3.**V. V. Buldygin and S. A. Solntsev,*Asymptotic Behavior of Linearly Transformed Sums of Random Variables*, Kluwer Academic Publishers, Dordrecht, 1997. MR**1471203 (98m:60002)****4.**V. V. Buldygin and M. K. Runovska,*On the convergence of series of autoregressive sequences*, Theory Stoch. Process.**15(31)**(2009), no. 1, 7-14. MR**2603166 (2011a:60116)****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