Multivariate extremal processes generated by independent non-identically distributed random variables

Let be the kth largest among X n1 , …, Xn [nt], where Xni = (Xi – an )/bn , {Xi } is a sequence of independent random variables and bn > 0 and an are norming constants. Suppose that for each converges in distribution. Then all the finite-dimensional laws of converge. The limiting process is represented in terms of a non-homogeneous two-dimensional Poisson process.