Precise Asymptotics in the Law of the Iterated Logarithm under Dependence
نویسنده
چکیده
Let {X n ; n ≥ 1} be a strictly stationary negatively associated sequence which satisfies EX 1 = 0, V ar(X 1) < ∞. Set S n = n k=1 X k , n ≥ 1, σ 2 = EX 2 1 + 2 ∞ k=2 EX 1 X k. In this paper, we prove that, for b > −1, lim ε0 ε 2(b+1) ∞ n=1 (log log n) b n log n P{|S n | ≥ εσ n log log n} = 2 b+1 (b + 1) √ π Γ(b + 3 2) holds if EX 2 1 (1 + log log |X 1 |) b−1 < ∞. The result of Gut and Spˇataru [2] is a special case of ours.
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