Limit results for maxima in non-stationary multivariate Gaussian sequences

AbstractLet {Xk, k⩾1} be a multivariate Gaussian sequence, and Mn be the partial maxima, taken componentwise, i.e. Mni=max{Xki,k⩽n}, for any i ⩽ p. We deal with the limiting behaviour of the distribution of Mn and show that, under certain conditions, this limit distribution is equal to the product of the marginal limit distributions of the Mni's or to the asymptotic product of the distributions of the Xk's