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

A. E. Kyprianou; P. Patie

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 917-928
  • ISSN: 0246-0203

Abstract

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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 features of fluctuation theory for spectrally negative Lévy processes (see, e.g., [In Séminaire de Probabalités XXXVIII (2005) 16–29 Springer]) as well as more recent fluctuation identities for positive self-similar Markov processes found in [Ann. Inst. H. Poincaré Probab. Statist.45 (2009) 667–684].

How to cite

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Kyprianou, A. E., and Patie, P.. "A Ciesielski–Taylor type identity for positive self-similar Markov processes." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 917-928. <http://eudml.org/doc/243211>.

@article{Kyprianou2011,
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, e.g., [In Séminaire de Probabalités XXXVIII (2005) 16–29 Springer]) as well as more recent fluctuation identities for positive self-similar Markov processes found in [Ann. Inst. H. Poincaré Probab. Statist.45 (2009) 667–684].},
author = {Kyprianou, A. E., Patie, P.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {positive self-similar Markov process; Ciesielski–Taylor identity; spectrally negative Lévy process; Bessel processes; stable processes; lamperti-stable processes; Ciesielski-Taylor identity; Lamperti-stable processes},
language = {eng},
number = {3},
pages = {917-928},
publisher = {Gauthier-Villars},
title = {A Ciesielski–Taylor type identity for positive self-similar Markov processes},
url = {http://eudml.org/doc/243211},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Kyprianou, A. E.
AU - Patie, P.
TI - A Ciesielski–Taylor type identity for positive self-similar Markov processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 917
EP - 928
AB - 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, e.g., [In Séminaire de Probabalités XXXVIII (2005) 16–29 Springer]) as well as more recent fluctuation identities for positive self-similar Markov processes found in [Ann. Inst. H. Poincaré Probab. Statist.45 (2009) 667–684].
LA - eng
KW - positive self-similar Markov process; Ciesielski–Taylor identity; spectrally negative Lévy process; Bessel processes; stable processes; lamperti-stable processes; Ciesielski-Taylor identity; Lamperti-stable processes
UR - http://eudml.org/doc/243211
ER -

References

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