This is a preview of subscription content, log in via an institution to check access.
Literature Cited
S. N. Bernshtein, “Extension of the limit theorem of probability theory to sums of independent variables,” in: Collected Works [in Russian], Nauka, Moscow (1964), pp. 121–176.
A. V. Bulinskii, “On the central limit theorem for random fields,” in: Second Vilnius Conference on Probability Theory and Mathematical Statistics [in Russian], Vol. 1, Vilnius (1977), pp. 69–70.
A. V. Bulinskii, “On the speed of convergence in the central limit theorem for additive random functions,” Dokl. Akad. Nauk SSSR,235, No. 4, 741–744 (1977).
V. A. Egorov, “Some limit theorems for m-dependent random variables,” Liet. Mat. Sb.,10, No. 1, 51–59 (1970).
W. Hoeffding and H. Robbins, “The central limit theorem for dependent random variables,” Duke Math. J.,15, 773–780 (1948).
I. A. Ibragimov, “Some limit theorems for stationary processes,” Teor. Veroyatn. Primen.,7, No. 4, 361–392 (1962).
V. A. Malyshev, “Central limit theorem for Gibbsian random fields,” Dokl. Akad. Nauk SSSR,224, No. 1, 35–38 (1975).
B. S. Nakhapetyan, “Central limit theorem for random fields satisfying a strong mixing condition,” Dokl. Akad. Nauk Arm. SSR, No. 4, 210–214 (1975).
V. V. Petrov, “On the central limit theorem for m-dependent random variables,” in: Memoirs of the All-Union Conference on Probability Theory and Mathematical Statistics, Erevan (1960), pp. 38–44.
W. Phillip, “The central limit theorem for mixing sequences of random variables,” Z. Wahr. Verw. Geb.,12, 155–171 (1969).
W. Phillip, “The Remainder in the central limit theorem for mixing stochastic processes,” Ann. Math. Statist.,40, 601–609 (1969).
B. A. Ryauba, “Estimate of the speed of convergence in the central limit theorem for random fields,” in: Second Vilnius Conference on Probability Theory and Mathematical Statistics [in Russian], Vol. 2, Vilnius (1977), pp. 144–145.
V. Statulevičius, “Limit theorems for dependent random variables under various regularity conditions,” in: Proceedings of the International Congress of Mathematicians, Vancouver (1975), pp. 173–181.
V. Statulevičius, “Application of semi-invariants to asymptotic analysis of distributions of random processes,” Multivariate Anal.,4, 325–337.
Ch. Stein, “A bound for the error in the Normal approximation to the distribution of a sum of dependent random variables,” in: Proc. Sixth Berkeley Symposium on Math. Statist. and Probability, Univ. of California Press, Berkeley (1973), pp. 583–602.
V. V. Shergin, “Estimate of the remainder term in the central limit theorem for m-dependent random variables,” Liet. Mat. Sb.,16, No. 4, 245–250 (1976).
A. N. Tikhomirov, “On the speed of convergence in the central limit theorem for weakly dependent variables,” Vestn. Leningr. Gos. Univ.,2, No. 7, 158–159 (1976).
Additional information
Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 20, No. 1, pp. 157–164, January–March, 1980.
Rights and permissions
About this article
Cite this article
Riauba, B. Speed of convergence in the central limit theorem for m-dependent random fields. Lith Math J 20, 71–75 (1980). https://doi.org/10.1007/BF00970858
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970858