Abelian theorems for a class of probability distributions inR d and their application

A class of multidimensional absolutely continuous distributions is considered. Each of them has a moment-generating function that is finite in a bounded set S and, therefore, generates a family of so-called conjugate or associated distributions. At the focus of our attention are the limiting distributions for this family that appear as the conjugating parameter tends to the boundary of S. As in the one-dimensional case, each such limiting distribution can be obtained as a consequence of an Abelian theorem. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.