Bernoulli

  • Bernoulli
  • Volume 19, Number 4 (2013), 1350-1377.

On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator

Francis Hirsch and Marc Yor

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Abstract

Results about the laws of the perpetuity and remainder variables associated to a subordinator are presented, with particular emphasis on their Mellin transforms, and multiplicative infinite divisibility property. Previous results by Bertoin–Yor (Electron. Commun. Probab. 6 (2001) 95–106) are incorporated in our discussion; important examples when the subordinator is the inverse local time of a diffusion are exhibited. Results of Urbanik (Probab. Math. Statist. 15 (1995) 493–513) are also discussed in detail; they appear to be too little known, despite the fact that quite a few of them have priority upon other works in this area.

Article information

Source
Bernoulli, Volume 19, Number 4 (2013), 1350-1377.

Dates
First available in Project Euclid: 27 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1377612855

Digital Object Identifier
doi:10.3150/12-BEJSP01

Mathematical Reviews number (MathSciNet)
MR3102555

Zentralblatt MATH identifier
1287.60096

Keywords
inverse local time Mellin transform multiplicative infinite divisibility perpetuity

Citation

Hirsch, Francis; Yor, Marc. On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. Bernoulli 19 (2013), no. 4, 1350--1377. doi:10.3150/12-BEJSP01. https://projecteuclid.org/euclid.bj/1377612855


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