Limiting behavior of the maximum of the partial sum for asymptotically negatively associated random variables under residual Cesaro alpha-integrability assumption

摘要

Asymptotically negative association is a special dependence structure. By relating such dependence condition to residual Cesaro alpha-integrability and to strongly residual Cesar alpha-integrability, some La-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.