Abstract
In this paper, we obtain the maximal inequalities for linear process, φ -mixing sequence and linearly negative quadrant dependent (LNQD) sequence when the r th moments of random variables are finite for r > 2 . Applying these maximal inequalities above, we get the Hájek–Rényi-type inequality, strong law of large numbers, strong growth rate and integrability of supremum for these three sequences.
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