On Free Regular and Bondesson Convolution Semigroups

A. Kuznetsov ()
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A. Kuznetsov: York University

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1493-1505

Abstract: Abstract Free regular convolution semigroups describe the distribution of free subordinators, while Bondesson class convolution semigroups correspond to classical subordinators with completely monotone Lévy density. We show that these two classes of convolution semigroups are in bijection with the class of complete Bernstein functions, and we establish an integral identity linking the two semigroups. We provide several explicit examples that illustrate this result.

Keywords: Free regular measure; Complete Bernstein function; Bondesson class; Subordinator; Kendall’s identity; Laplace transform; Cauchy transform; Bessel functions; Lambert W-function; 60G51; 46L54 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00909-w

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