Open Access
Translator Disclaimer
September 2013 On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator
Francis Hirsch, Marc Yor
Bernoulli 19(4): 1350-1377 (September 2013). DOI: 10.3150/12-BEJSP01

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.

Citation

Download Citation

Francis Hirsch. Marc Yor. "On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator." Bernoulli 19 (4) 1350 - 1377, September 2013. https://doi.org/10.3150/12-BEJSP01

Information

Published: September 2013
First available in Project Euclid: 27 August 2013

zbMATH: 1287.60096
MathSciNet: MR3102555
Digital Object Identifier: 10.3150/12-BEJSP01

Keywords: inverse local time , Mellin transform , multiplicative infinite divisibility , perpetuity

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.19 • No. 4 • September 2013
Back to Top