Resumen de Mean Convergence Theorems for Weighted Sums of Arrays of Residually h -integrable Random Variables Concerning the Weights under Dependence Assumptions

Demei Yuan, Bao Tao

• From the classical notion of uniform integrability of a sequence of random variables, a new concept called residual h-integrability is introduced for an array of random variables, concerning an array of constants, which is weaker than other previous related notions of integrability.

  Martingale difference, pairwise negative quadrant dependence, tail ?-mixing property and L p -mixingale are four special kinds of dependence structures, where 1?p?2. By relating the residual h-integrability with such these dependence assumptions, some conditions are formulated under which mean convergence theorems for weighted sums of arrays of random variables are established, and many earlier results are explained as the special cases of the ones appearing in our present work.