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Some limit theorems for m -pairwise negative quadrant dependent random variables

Yongfeng Wu, Jiangyan Peng (2018)

Kybernetika

The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent p ( 1 p 2 ) for m -pairwise negatively quadrant dependent ( m -PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise m -PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be solved easily...

Some mean convergence and complete convergence theorems for sequences of m -linearly negative quadrant dependent random variables

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2013)

Applications of Mathematics

The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of m -linearly negative quadrant dependent random variables ( m = 1 , 2 , ). For a sequence of m -linearly negative quadrant dependent random variables { X n , n 1 } and 1 < p < 2 (resp. 1 p < 2 ), conditions are provided under which n - 1 / p k = 1 n ( X k - E X k ) 0 in L 1 (resp. in L p ). Moreover, for 1 p < 2 , conditions are provided under which n - 1 / p k = 1 n ( X k - E X k ) converges completely to 0 . The current work extends some results of Pyke and Root (1968) and it extends and improves some...

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