Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law

Assuming that the sample correlation matrix of vector XX converges to a positive definite nonstochastic matrix, we establish a uniform Euclidean norm approximation in probability and a functional CLT for a multivariate Student process, based on independent copies of XX. These results obtain if and only if XX is in the generalized domain of attraction of the multivariate normal law.