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On Free Regular and Bondesson Convolution Semigroups

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  • A. Kuznetsov

    (York University)

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.

Suggested Citation

  • A. Kuznetsov, 2020. "On Free Regular and Bondesson Convolution Semigroups," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1493-1505, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00909-w
    DOI: 10.1007/s10959-019-00909-w
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    References listed on IDEAS

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    1. Victor Pérez-Abreu & Noriyoshi Sakuma, 2012. "Free Infinite Divisibility of Free Multiplicative Mixtures of the Wigner Distribution," Journal of Theoretical Probability, Springer, vol. 25(1), pages 100-121, March.
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