A Ciesielski–Taylor type identity for positive self-similar Markov processes
A. E. Kyprianou, P. Patie (2011)
Annales de l'I.H.P. Probabilités et statistiques
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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...