In this paper, Kolmogorov-type inequality for negatively superadditive dependent (NSD) random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated (NA) sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.
In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.
In this paper, we get the Hjek-Rényi-type inequalities for a pairwise NQD sequence, an Lr (r > 1) mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for Lr (r > 1) mixingale of Hansen.
