Stable laws and Beurling kernels

Abstract

We identify a close relation between stable distributions and the limiting homomorphisms central to the theory of regular variation. In so doing some simplifications are achieved in the direct analysis of these laws in Pitman and Pitman (2016); stable distributions are themselves linked to homomorphy.

Version with section 4 and Appendix omitted to appear in Adv. Appl. Prob. 48A (2016)