文档介绍：Hindawi Publishing CorporationJournal of Probability and StatisticsVolume 2010, Article ID 764043,17pagesdoi: plete Convergence for Maximal Sums ofNegatively Associated Random VariablesVictor M. KruglovDepartment of Statistics, Faculty putational Mathematics and ics,Moscow State University, Vorobyovy Gory, GSP-1, 119992, Moscow, RussiaCorrespondence should be addressed to Victor M. Kruglov,******@Received 24 December 2009; Accepted 1 April 2010Academic Editor: Mohammad Fraiwan Al-SalehCopyrightq2010 Victor M. Kruglov. This is an open access article distributed under the mons Attribution License, which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly and su?cient conditions are given for plete convergence of maximal sums ofidentically distributed negatively associated random variables. The conditions are expressed interms of integrability of random variables. Proofs are based on new maximal inequalities for sumsof bounded negatively associated random . IntroductionThe paper by Hsu and Robbins?1?initiated a great interest to plete convergenceof sums of independent random variables. Their research was continued by Erd¨os?2,3?,Spitzer?4?, and Baum and Katz?5?. Kruglov et al.?6?proved two general theorems thatprovide su?cient conditions for plete convergence for sums of arrays of row-wiseindependent random variables. In the paper of Kruglov and Volodin?7?, a criterion wasproved for plete convergence of sums of independent identically distributed randomvariable in a rather general setting. Taylor et al.?8?and Chen et al.?9,10?demonstrated thatmany known su?cient conditions plete convergence of sums of independent randomvariables can be transformed to su?cient conditions for plete convergence of sums ofnegatively associated random variables. Here we give necessary and su?cient conditions plete convergence of maximal sums of negatively associated identic