Some mean convergence and complete convergence theorems for sequences of \(m\)-linearly negative quadrant dependent random variables. (Q2444510)

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.