Abstract
Let X, X 1 , X 2 , ... be i.i.d. random variables with EX = 0, and set S n = X 1 + ... + X n . We prove that, for 1 < p < 3/2, formula math. under the assumption that EX 2 = σ 2 and E[|X| 2p (log + |X|) -p ] < ∞. Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
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