Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

Let {Xni,Fni;1≤i≤n,n≥1} be an array of Rdmartingale difference random vectors and {Ani,1≤i≤n,n≥1} be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2) moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.