Limiting Behavior of the Maximum of the Partial Sum for Linearly Negative Quadrant Dependent Random Variables under Residual Cesàro Alpha-Integrability Assumption

Abstract

Linearly negative quadrant dependence is a special dependence structure. By relating such conditions to residual Cesàro alpha-integrability assumption, as well as to strongly residual Cesàro alpha-integrability assumption, some $L_p$-convergence and complete convergence results of the maximum of the partial sum are derived, respectively.