Geodesic
A note on the Kolmogorov--Marcinkiewicz--Zygmund type strong law of large numbers for elements of autoregression sequences
Teoriâ slučajnyh processov, Tome 22 (2017) no. 1, pp. 22-29.

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In the paper we consider the Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers for sums whose terms are elements of regression sequences of random variables. Some necessary and sufficient conditions providing SLLN are obtained in terms of coefficients of the regression sequence. Several special cases of regression sequences are considered as well.
Keywords: Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers, autoregression sequences of random variables, sums of random variables. 
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M. K. Ilienko. A note on the Kolmogorov--Marcinkiewicz--Zygmund type strong law of large numbers for elements of autoregression sequences. Teoriâ slučajnyh processov, Tome 22 (2017) no. 1, pp. 22-29. http://geodesic.mathdoc.fr/item/THSP_2017_22_1_a2/

[1] A. de Acosta, “Inequalities for $B$-valued random vectors with applications to the law of large numbers”, Ann.Probab., 9 (1981), 157–161 | DOI | MR | Zbl

[2] Theory Probab. Appl., 26, 573–580 | DOI | MR | Zbl

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

[4] M. Runovska, “The convergence of series whose terms are elements of multidimensional Gaussian Markov sequences”, Theor. Probability and Math. Statist., 84 (2012), 139–150 | DOI | MR | Zbl

[5] V. Buldygin, M. Runovska (M. Ilienko), Sums whose terms are elements of linear random regression sequences, Lambert Academic Publishing, 2014

[6] Deli Li, Yongcheng Qi, A. Rosalsky, “A refinement of the Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers”, J. Theor. Probab., 24 (2011), 1130–1156 | DOI | MR | Zbl

[7] A. Gut, “A contribution to the theory of asymptotic martingales”, Glasg. Math.J., 23 (1982), 177–186 | DOI | MR | Zbl

[8] F. Hechner, B. Heinkel, “The Marcinkiewicz-Zygmund LLN in Banach spaces: a generalized martingale approach”, J. Theor. Probab., 23 (2010), 509–522 | DOI | MR | Zbl

[9] M. Ilienko, “A refinement of conditions for the almost sure convergence of series of multidimensional regression sequences”, Theor. Probability and Math. Statist., 93 (2016), 71–78 | DOI | MR | Zbl

[10] J. P. Kahane, Some random series of functions, Cambridge Univ. Press, Heath, Cambridge, 1985 | MR | Zbl

[11] A. Kolmogorov, “Sur la loi forte des grands nombres”, C.R. Acad. Sci. Paris., 191:20 (1930), 910–912

[12] J. Marcinkiewicz, A. Zygmund, “Sur les fonctions independantes”, Fund. Mat., 29 (1937), 60–90 | MR

[13] E. Mourier, “Eléments aléatoires dans un espace de Banach”, Ann. Inst. H. Poincaré, 19 (1953), 161–244 | MR