WEAK CONVERGENCE OF RANDOM VECTORS AND DISTRIBUTIONSIN BANACH SPACES
Ryszard Jajte Adam Paszkiewicz
Abstract: Let be a sequence of random vectors with values in a Banach space with
distributions weakly converging to a given distribution We characterize a general
form of a distribution of a weak limit of in Banach space of Bochner integrable
vectors. We show that the weak convergence of random vectors in implies that
stochastically. Moreover, the conditions
stochastically and stochastically for any are equivalent.