TL;DR
This paper explores the connection between stable distributions and homomorphisms in regular variation, simplifying their analysis and revealing their intrinsic link to homomorphic structures.
Contribution
It establishes a novel relationship between stable laws and limiting homomorphisms, enhancing understanding of their structural properties.
Findings
Stable distributions are linked to homomorphy.
Simplifications in analyzing stable laws are achieved.
The connection clarifies the structural nature of stable laws.
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.
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