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Abstrakty
In this paper we obtain the conditions of the strong law of large numbers for two-dimensional arrays of random variables which are blockwise independent and blockwise orthogonal. Some well-known results on the strong laws of large numbers for two-dimensional arrays of random variables are extended.
Czasopismo
Rocznik
Tom
Strony
385--391
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An 42118, Vietnam
autor
- Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An 42118, Vietnam
Bibliografia
- [1] R. P. Agnew, On double orthogonal series, Proc. London Math. Soc. 33 (1932), pp. 420-434.
- [2] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 3rd edition, Springer, New York 1997.
- [3] V. F. Gaposhkin, On series of blockwise independent and blockwise orthogonal systems (in Russian), Matematika 5 (1990), pp. 12-18.
- [4] V. F. Gaposhkin, On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables, Theory Probab. Appl. 39 (1995), pp. 677-684.
- [5] D. H. Hong and S. Y. Hwang, Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables, Int. J. Math. Math. Sci. 22 (1999), pp. 171-177.
- [6] D. H. Hong and A. I. Volodin, Marcinkiewicz-type law of large numbers for double array, J. Korean Math. Soc. 36 (1999), pp. 1133-1143.
- [7] F. Móricz, Moment inequalities for the maximum of partial sums of random fields, Acta Sci. Math. 39 (1977), pp. 353-366.
- [8] F. Móricz, Strong limit theorems for blockwise m-dependent and blockwise quasiorthogonal sequences of random variables, Proc. Amer. Math. Soc. 101 (1987), pp. 709-715.
- [9] M. J. Wichura, Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters, Ann. Math. Statist. 60 (1969), pp. 681-687.
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Bibliografia
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