Highly Influenced

12 Excerpts

- Published 2009

The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly some classical features of fluctuation theory for spectrally negative Lévy processes (see eg. [15]) as well as more recent fluctuation identities for positive self-similar Markov processes found in Patie [19].

@inproceedings{Kyprianou2009ACT,
title={A Ciesielski-Taylor type identity for positive self-similar Markov processes},
author={Andreas E. Kyprianou},
year={2009}
}