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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
Posted:
February 2, 2012
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Abstract: We find necessary and sufficient conditions for the almost sure convergence of sums of centered Gaussian Markov sequences.
References
- 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:
http://dx.doi.org/10.1090/S0094-9000-2012-00848-X
PII:
S 0094-9000(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):
17/MAY/2010
Posted:
February 2, 2012
Article copyright:
© Copyright 2012 American Mathematical Society
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