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

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

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

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topKyprianou, 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 -

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