Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors - Wu, Yi; Wang, Xue Jun (Acta mathematica Sinica. English series, 2024)
Let be an array of martingale difference random vectors and 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.