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

@article{Kyprianou2011ACT, title={A Ciesielski–Taylor type identity for positive self-similar Markov processes}, author={Andreas E. Kyprianou and P. Patie}, journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques}, year={2011}, volume={47} }

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 Levy processes into itself. Secondly, some classical…

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