A new ideal metric with applications to multivariate stable limit theorems

Summary A new ideal metric of orderr>1 is introduced on ^k and a thorough analysis of its metric properties is given. In comparison to the known ideal metric of Zolotarev this new metric allows estimates from above by pseudo difference moments and thus allows applications to stable limit theorems. As applications we give the right order Berry-Esséen type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound Poisson distributions.Research supported by NATO GRANT CRG 900 798 and by a DFG Grant