On the convergence of series of autoregressive sequences
Teoriâ slučajnyh processov, Tome 15 (2009) no. 1, pp. 7-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions for the almost sure convergence of a series of autoregressive sequences are studied. In particular, the convergence of a series of zero-mean Gaussian Markov sequences are considered.
Keywords: Autoregressive sequences, Gaussian Markov sequences, summability theory, almost sure convergence of series of random variables.
@article{THSP_2009_15_1_a1,
     author = {Valerii. V. Buldygin and Marina. K. Runovska},
     title = {On the convergence of series of autoregressive sequences},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {7--14},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a1/}
}
TY  - JOUR
AU  - Valerii. V. Buldygin
AU  - Marina. K. Runovska
TI  - On the convergence of series of autoregressive sequences
JO  - Teoriâ slučajnyh processov
PY  - 2009
SP  - 7
EP  - 14
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a1/
LA  - en
ID  - THSP_2009_15_1_a1
ER  - 
%0 Journal Article
%A Valerii. V. Buldygin
%A Marina. K. Runovska
%T On the convergence of series of autoregressive sequences
%J Teoriâ slučajnyh processov
%D 2009
%P 7-14
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a1/
%G en
%F THSP_2009_15_1_a1
Valerii. V. Buldygin; Marina. K. Runovska. On the convergence of series of autoregressive sequences. Teoriâ slučajnyh processov, Tome 15 (2009) no. 1, pp. 7-14. http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a1/

[1] V. V. Buldygin, S. A. Solntsev, Functional methods in problems of the summation of random variables, Naukova Dumka, Kiev, 1989 | MR | Zbl

[2] V. V. Buldygin, S. A. Solntsev, Asymptotic behavior of linearly transformed sums of random variables, Kluwer, Dordrecht, 1997 | MR

[3] R. G. Cooke, Infinite matrices and sequence spaces, MacMillan, London, 1950 | MR | Zbl

[4] W. Feller, Introduction to probability theory and its applications, v. 2, Wiley, New York, 1971 | MR | Zbl

[5] J. P. Kahane, Some random series of functions, Heath, Lexington, D.C., 1968 | MR | Zbl

[6] A. N. Kolmogorov, S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999