Literature Cited
A. P. Basu, “On the rate of convergence to normality for sums of dependent random variables,” Acta Math. Acad. Sci. Hung.,28, 261–265 (1976).
P. Billingsley, Convergence of Probability Measures, Wiley (1976).
J. L. Doob, Stochastic Processes, Wiley (1953).
M. Loeve, Probability Theory, Van Nostrand (1963).
R. M. Loynes, “The central limit theorem for backwards martingales,” Z. Wahr. Verw. Geb.,13, 1–8 (1969).
R. M. Loynes, “An invariance principle for reversed martingales,” Proc. Am. Math. Soc.,25, 56–64 (1970).
D. McLeish, “Dependent central limit theorems and invariance principles,” Ann. Prob.,2, 620–628 (1974).
B. L. S. Prakasa Rao, “On central limit theorems for backwards martingale arrays,” Proc. 41st Session Bull. Int. Statist. Inst.,37, 697–700 (1977).
C. Stone, “Weak convergence of stochastic processes defined on semi-infinite time intervals,” Proc. Am. Math. Soc.,14, 694–696 (1963).
D. Scott, “An invariance principle for reversed martingales,” Z. Wahr. Verw. Geb.,20, 9–27 (1971).
Additional information
Indian Statistical Institute, New Delhi. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 19, No. 4, pp. 153–165, October–December, 1979.
Rights and permissions
About this article
Cite this article
Rao, B.L.S.P. Central limit theorems, invariance principle, and rates of convergence for backwards martingale arrays. Lith Math J 19, 538–546 (1979). https://doi.org/10.1007/BF00970728
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970728