TY - CHAP

T1 - A Transformation for Spectrally Negative Lévy Processes and Applications

AU - Chazal, Marie

AU - Kyprianou, Andreas E.

AU - Patie, Pierre

PY - 2021/7/30

Y1 - 2021/7/30

N2 - The aim of this work is to extend and study a family of transformations between Laplace exponents of Lévy processes which have been introduced recently in a variety of different contexts, Patie (Bull Sci Math 133(4):355–382, 2009; Bernoulli 17(2):814–826, 2011), Kyprianou and Patie (Ann Inst H Poincar’ Probab Statist 47(3):917–928, 2011), Gnedin (Regeneration in Random Combinatorial Structures. arXiv:0901.4444v1 [math.PR]), Patie and Savov (Electron J Probab 17(38):1–22, 2012), as well as in older work of Urbanik (Probab Math Statist 15:493–513, 1995). We show how some specific instances of this mapping prove to be useful for a variety of applications.

AB - The aim of this work is to extend and study a family of transformations between Laplace exponents of Lévy processes which have been introduced recently in a variety of different contexts, Patie (Bull Sci Math 133(4):355–382, 2009; Bernoulli 17(2):814–826, 2011), Kyprianou and Patie (Ann Inst H Poincar’ Probab Statist 47(3):917–928, 2011), Gnedin (Regeneration in Random Combinatorial Structures. arXiv:0901.4444v1 [math.PR]), Patie and Savov (Electron J Probab 17(38):1–22, 2012), as well as in older work of Urbanik (Probab Math Statist 15:493–513, 1995). We show how some specific instances of this mapping prove to be useful for a variety of applications.

KW - Exponential functional

KW - Fluctuation theory

KW - Hypergeometric function

KW - Intertwining

KW - Positive self-similar Markov process

KW - Spectrally negative Lévy process

UR - http://www.scopus.com/inward/record.url?scp=85122451886&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-83309-1_9

DO - 10.1007/978-3-030-83309-1_9

M3 - Chapter or section

AN - SCOPUS:85122451886

SN - 9783030833084

T3 - Progress in Probability

SP - 157

EP - 180

BT - A Lifetime of Excursions Through Random Walks and Lévy Processes

A2 - Chazal, M.

A2 - Kyprianou, A. E.

A2 - Patie, P.

PB - Birkhauser

CY - Cham, Switzerland

ER -