Hajek–Renyi-type inequality and strong law of large numbers for END sequences

Complete convergence of randomly weighted END sequences and its application

“…In view of the importance of END random variables, many researchers pay attention to the study of END. For example, Liu [ 1 , 8 ] studied the precise large deviations and moderate deviations of END sequence with heavy tails; Chen et al [ 9 ] obtained strong law of large numbers of END sequence and gave some applications to the risk theory and renewal theory; Shen [ 10 ] obtained some moment inequalities of END sequence; Wang et al [ 11 ] and Hu et al [ 12 ] investigated the complete convergence for END sequences; Wang et al [ 13 ] and Yang et al [ 14 ] investigated the nonparametric regression model under END errors; Yang et al [ 15 ] obtained some large deviation results of nonlinear regression models under END errors; Wang et al [ 16 ] established some exponential inequality for m -END sequence; Deng et al [ 17 ] studied the Hajek-Renyi-type inequality and strong law of large numbers for END sequences, etc. Furthermore, there are many works on the negatively dependent random variables.…”

Hajek–Renyi-type inequality for $(\alpha , \beta )$-mixing sequences and its application to change-point model

“…Wan [24] established the Hajek-Renyi inequality for ρ-mixing sequences. Deng et al [4] studied the Hajek-Renyi-type inequality for 0 < p ≤ 2 for a sequence of extended negatively dependent (END) random variables.…”