Borel-cantlli Lemmas And The Strong Convergence Of Weighted Sums Of Widely Dependent Random Variables

It is well known that strong convergence theory and Borel-Cantlli lemmas are thehot research issues in probabilistic theory, scholars concentrated on the issue for along time, and many results in this field have been obtained. In this paper, based onthe work of Wang et al.(2011,b), we study the strong convergence of weighted sumsand Borel-Cantlli lemmas under some fairly weak conditions, and get some results ona.s.convergence and complete convergence. Additionally, we obtain some Borel-Cantllilemmas for WD r.v.s and some corollaries, which extend related results of Wang etal.(2011, b)from NA case to WD case. The above-mentioned widely dependent r.v.scontain common negatively dependent r.v.s, some positively dependent r.v.s and someothers, hence the obtained results extend and improved some existing results greatly.