Complete convergence for weighted sums of NA sequences

On convergence for sequences of pairwise negatively quadrant dependent random variables

“…The next corollary is similar to Theorem 1.1 of Liang and Su [11]. However, we consider pairwise NQD instead of NA, and our result does not require the moments of order p > 2 of random variables {X n , n 1} to exist.…”

Complete convergence for weighted sums of pairwise independent random variables

“…random variables; Li et al [6] obtained complete convergence of weighted sums without identically distributed assumption. Liang and Su [7] extended the the results of Thrum [5] and Li et al [6], and showed the complete convergence of weighted sums of negatively associated sequence. Beak [8] discussed the almost sure convergence for weighted sums of pairwise independent random variables.…”

The rates in complete moment convergence for negatively associated sequences

“…(log n) The moment condition E X 2 1 (log |X 1 |) δ < ∞ is used as follows, note the corresponding part of 9 , we have we then complete the proof of (3.5). Finally, observe that…”

“…Under appropriate conditions, lots of results have been obtained for negatively associated sequences, the central limit theorem (CLT) [13], probability inequalities [15,17], weak convergence [19,20], almost sure convergence [12], law of the iterated logarithm (LIL) [16] and complete convergence [8,9], precise rates [5,21,22].…”