Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.