For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results...

The main objective for this paper is twofold. We first present a method for the derivation of an arbitrarily exact approximation to the distribution of Cramér-von Mises type functionals of any given Gaussian process X = {X(t): 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1}....