an:06282094
Zbl 1299.60047
Wu, Yongfeng; Rosalsky, Andrew; Volodin, Andrei
Some mean convergence and complete convergence theorems for sequences of \(m\)-linearly negative quadrant dependent random variables
EN
Appl. Math., Praha 58, No. 5, 511-529 (2013); correction ibid. 62, No. 2, 209-211 (2017).
00331561
2013
j
60F15 60F25
\(m\)-linearly negative quadrant dependence; \(L_p\)-convergence; complete convergence
In the paper, a new type of dependence in a sequence of random variables \(\{X_n:n\geq 1\}\), called \(m\)-linear negative quadrant dependence, is introduced. For such variables, the convergence of \(n^{-1/p}\sum _{k=1}^n (X_k-\operatorname{E} X_k)\) to zero is proved in \(L_p\) and in the sense of complete convergence if \(1 \leq p < 2.\) A Kolmogorov-type exponential inequality is also established as a by product.
Zuzana Pr????kov?? (Praha)