Operator-normed sums of independent random vectors

Abstract

Both types of normalizations, scalar and operator, may be employed for studying limit theorems for sums of independent random vectors. The limit theorems with scalar normalizations have been much investigated and form the basis of classical probability theory. At the same time, it has not been until recently when studying operator normalizations (especially in the framework of almost sure convergence) began, though these normalizations are more adequate for reflecting the asymptotic behaviour of sums of independent random vectors.