A Ciesielski-Taylor type identity for positive self-similar Markov processes

Abstract

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].

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