Regular Variation and the Functional Central Limit Theorem for Heavy Tailed Random Vectors


Mark_M. Meerschaert, Steven_J. Sepanski


Multivariable regular variation is used, along with the martingale central limit theorem, to give a very simple proof that the partial sum process for a sequence of independent, identically distributed random vectors converges to a Brownian motion whenever the summands belong to the generalized domain of attraction of a normal law. This includes the heavy tailed case, where the covariance matrix is undefined because some of the marginals have infinite variance.