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Stable laws and Beurling kernels

Part of: Difference equations Real functions Stability theory Difference and functional equations Distribution theory - Probability

Published online by Cambridge University Press:  25 July 2016

Adam J. Ostaszewski
Adam J. Ostaszewski*
Affiliation:
London School of Economics
*
Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, UK. Email address: a.j.ostaszewski@lse.ac.uk
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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.

Keywords

Stable lawsBeurling regular variationquantifier weakeninghomomorphismGoldie equationGołąb‒Schinzel equationLevi‒Civita equation

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 26A03: Foundations 39B22: Equations for real functions 34D05: Asymptotic properties 39A20: Multiplicative and other generalized difference equations, e.g. of Lyness type
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 239 - 248
Copyright
Copyright © Applied Probability Trust 2016 

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