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Let \(\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}\) be a random field of negatively dependent random variables. The complete convergence results for negatively dependent random fields are refined. To obtain the main theorem several lemmas for convergence of families indexed by \(\mathbb{N}^d\) have been proved. Auxiliary lemmas have wider application to study the random walks on the lattice.
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2018
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2018-12-22
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Bibliografia
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- Gut, A., Stadtmuller, U., On the Hsu-Robbins-Erdos-Spitzer-Baum-Katz theorem for random fields, J. Math. Anal. Appl. 387 (1) (2012), 447-463.
- Hsu, P. L., Robbins, H., Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31.
- Klesov, O. I., The strong law of large numbers for multiple sums of independent identically distributed random variables, Matem. Zametki 38 (1985), 915-930 (English transl. in Math. Notes 38 (1986), 1006-1014).
- Klesov, O. I., Limit Theorems for Multi-Indexed Sums of Random Variables, Springer-Verlag, Berlin-Heidelberg, 2014.
- Łagodowski, Z. A., An approach to complete convergence theorems for dependent random fields via application of Fuk–Nagaev inequality, J. Math. Anal. Appl. 437 (2016), 380-395.
- Lehmann, E. L., Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153.
- Neveu, J., Discrete-Parameter Martingales, North-Holland, Amsterdam; American Elsevier, New York, 1975.
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bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_1