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

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

2009-08-08

arxiv.org/abs/0908.1157v2

Mathematics

Probability

Scientific paper

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 L\'evy processes into itself. Secondly some classical features of fluctuation theory for spectrally negative L\'evy processes as well as more recent fluctuation identities for positive self-similar Markov processes.

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