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A Central Limit Theorem with Conditioning on the Distant Past

Published online by Cambridge University Press:  20 November 2018

D. L. McLeish
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Serfling (1968) has considered a central limit theorem in which assumptions are made concerning the expectation of variables conditioned on their distant predecessors. Dvoretsky (1972, theorem 5.3) has continued this investigation. Serfling showed that both martingales and φ-mixing sequences satisfied his conditions, and Dvoretsky extended this to Strong mixing sequences of random variables.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 245 - 247
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Chung, K. L., A course in probability theory, Harcourt, Brace and World inc., (1968).Google Scholar
2. Dvoretsky, A., Central limit theorems for dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Prob. U of California Press, (1972), 513-535.Google Scholar
3. McLeish, D. L., Invariance principles for dependent random variables. Zeit für Wahr (to appear).Google Scholar
4. Serfling, R. J., Contributions to central limit theory for dependent variables. Ann. Math. Statist. 39 (1968), 1158-1175.Google Scholar