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

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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. 
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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