On complete convergence for L^p‐mixingales

Abstract

Abstract. We provide in this paper sufficient conditions for the complete convergence for the partial sums and the random selected partial sums of B-valued L p -mixingales.

Complete convergence theorems for L-mixingales

“…The sufficient conditions employed in this paper are much more easier to be verified than those used in [27], while some cases that Hu [27] did not discuss are also fully studied here. In an important particular setup, the necessary conditions are also discussed (see Remark 2.2 below).…”

“…Gan [18] extended the results of De Jong [13] from the case of partial sums to the case of weighted sums. Hu [27] gave some more general sufficient conditions for the complete convergence for B-valued L p -mixingales.…”