Convergence of series of Gaussian Markov sequences
Author:
M. K. Runovska
Translated by:
O. Klesov
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
Full-text PDF Free Access
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Additional Information
Abstract: We find necessary and sufficient conditions for the almost sure convergence of sums of centered Gaussian Markov sequences.
References
- 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, 156–157 (Russian, with English summary). MR 0494429
- V. V. Buldygin and S. A. Solntsev, Funktsional′nye metody v zadachakh summirovaniya sluchaĭ nykh velichin, “Naukova Dumka”, Kiev, 1989 (Russian). MR 1007589
- 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
- Valerii V. Buldygin and Marina K. Runovska, On the convergence of series of autoregressive sequences, Theory Stoch. Process. 15 (2009), no. 1, 7–14. MR 2603166
- N. N. Vorob′ev, Teoriya ryadov, “Nauka”, Moscow, 1979 (Russian). Fourth edition, revised and augmented; Izbrannye glavy vyssheĭ matematiki dlya inzhenerov i studentov vtuzov. [Selected Chapters in Higher Mathematics for Engineers and Technical University Students]. MR 548875
References
- 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)
- 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)
- 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)
- 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)
- 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
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
