Abstract
Let {X, X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set \(S_n = \sum\nolimits_{k = 1}^n X _k ,M_n = max_{k \leqslant n} \left| {S_k } \right|,n \geqslant 1\). Suppose lim n→∞ \(ES_n^2 /n = :\sigma ^2 > 0\) and \(\sum\limits_{n = 1}^\infty {\rho ^{2/d} \left( {2^n } \right)} < \infty \), where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,
, where Γ(•) is a Gamma function.
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Research supported by the National Natural Science Foundation of China (10071072).
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Wei, H., Lixin, Z. & Ye, J. Precise rate in the law of iterated logarithm for ρ-mixing sequence. Appl. Math. Chin. Univ. 18, 482–488 (2003). https://doi.org/10.1007/s11766-003-0076-4
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DOI: https://doi.org/10.1007/s11766-003-0076-4