Geodesic
A Central Limit Theorem with Conditioning on the Distant Past
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 245-247

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
A Central Limit Theorem with Conditioning on the Distant Past. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 245-247. doi: 10.4153/CMB-1975-047-5
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[1] 1. Chung, K. L., A course in probability theory, Harcourt, Brace and World inc., (1968). Google Scholar

[2] 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] 3. McLeish, D. L., Invariance principles for dependent random variables. Zeit für Wahr (to appear). Google Scholar

[4] 4. Serfling, R. J., Contributions to central limit theory for dependent variables. Ann. Math. Statist. 39 (1968), 1158-1175. Google Scholar

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