V. V. Buldygin, V. A. Koval

Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes

The problems of almost sure convergence to zero and almost sure boundedness of operator-normed sums of different sequences of random vectors are studied. The sequences of independent random vectors, orthogonal random vectors and the sequences of vector-valued martingale-differences are considered. General results are applied to the problem of asymptotic behaviour of multidimensional autoregression processes.