Maximal inequalities for some dependent sequences and their applications

In this paper, we obtain the maximal inequalities for linear process, φφ-mixing sequence and linearly negative quadrant dependent (LNQD) sequence when the rrth moments of random variables are finite for r>2r>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.