Abstract
Asymptotically negative association is a special dependence structure. By relating such dependence condition to residual Cesàro alpha-integrability and to strongly residual Cesàro alpha-integrability, some Lp-convergence and complete convergence results of the maximum of the partial sum are derived, respectively. In addition, some of these conclusions are based on a new Rosenthal type inequality concerning asymptotically negatively associated random variables, which is of independent interest.
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