A Note on Moment Convergences for B-valued Martingale Random Variables

In this paper, a kind of the problems with respect to the moment complete convergence of martingale random variables is discussed. Under certain moment condition, based on high order moment and inequality of supmartingale and other relevant analytical methods, the sufficient condition of the moment complete convergence for martingale random variables is obtained. Therefor, the relation between moment and complete convergence for martingale random variables is revealed with a satisfying result.