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

Francis Hirsch; Marc Yor

doi:10.3150/12-bejsp01

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arXiv · 1309.7801

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

Francis Hirsch·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.

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Francis Hirsch, Marc Yor. 2013-09-30. On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. https://doi.org/10.3150/12-bejsp01

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