Article PDF
References
Billingsley, P.: Convergence of Probability Measures. New York: Wiley, 1968
Brown, B.M.: Martingale Central Limit Theorems. Ann. Math. Statist. 42, 59–66 (1971)
Davydov, Y.A.: Convergence of Distributions Generated by Stationary Stochastic Processes. Theor. Probability Appl. 8, 691–696 (1968)
Davydov, Y. A.: The Invariance Principle for Stationary Processes. Theor. Probability Appl. 15, 487–498 (1970)
Doob, J.L.: Stochastic Processes. New York: Wiley, 1953
Dvoretsky, A.: Asymptotic Normality for Sums of Dependent Random Variables. Proc. Sixth Berkeley Sympos. Math. Statist. Prob., Univ. Calif., II, 2, 513–535 (1972)
Feller, W.: An Introduction to Probability Theory and its Applications, Vol. II, second edition. New York: Wiley 1971
Knopp, K.: Theory and application of Infinite Series. 2nd Ed. London: Blackie 1941
Heyde, C.C.: On the Central Limit Theorem and Iterated Logarithm Law for Stationary Processes. Bull. Austral. Math. Soc. (to appear)
Loynes, R.M.: The Central Limit Theorem for Backward Martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 13, 1–8 (1969)
McLeish, D. L.: Dependent Central Limit Theorems and Invariance Principles. Ann. Probability 2, 620–628 (1974)
McLeish, D.L.: A Maximal Inequality and Dependent Strong Laws. Ann. Prob., to appear
Renyi, A.: On Mixing Sequences of Random Variables. Acta Math. Acad. Sci. Hungar. 9, 389–393 (1958)
Serfling, R.J.: Contributions to Central Limit Theory For Dependent Variables. Ann. Math. Statist. 39, 1158–1175 (1968)
Stone, C.: Weak Convergence of Stochastic Processes defined on Semi-infinite Time intervals. Proc. Amer. Math. Soc. 14, 694–696 (1963)
Scott, D.J.: Central Limit Theorem for Martingales and for Processes with Stationary Increments using A Skorokhod Representation Approach. Advances in Appl. Probability 5, 119–137 (1973)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McLeish, D.L. Invariance principles for dependent variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 32, 165–178 (1975). https://doi.org/10.1007/BF00532611
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00532611