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A. Kuznetsov, A. Kyprianou, J. Pardo (2010)
Meromorphic Lévy processes and their fluctuation identities.Annals of Applied Probability, 22
M. Caballero, L. Chaumont (2006)
Conditioned stable Lévy processes and the Lamperti representationJournal of Applied Probability, 43
A. Kuznetsov (2011)
On the density of the supremum of a stable processStochastic Processes and their Applications, 123
F. Hubalek, A. Kuznetsov (2010)
A convergent series representation for the density of the supremum of a stable processElectronic Communications in Probability, 16
P. Carmona, F. Petit, M. Yor (1997)
Exponential Functionals and Principal Values Related to Brownian Motion
México (2009)
On the asymptotic behaviour of increasing self-similar Markov processes
J. Lawrie, A. King (1994)
Exact solution to a class of functional difference equations with application to a moving contact line flowEuropean Journal of Applied Mathematics, 5
J. Lamperti (1972)
Semi-stable Markov processes. IZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 22
E. Barnes (1899)
The Genesis of the Double Gamma FunctionsProceedings of The London Mathematical Society
Maria Caballero, L. Chaumont (2004)
Weak convergence of positive self-similar Markov processes and overshoots of Lévy processesAnnals of Probability, 34
R. Wolpert (2000)
Lévy Processes
L. Chaumont, J. Pardo (2006)
The Upper Envelope of Positive Self-Similar Markov ProcessesJournal of Theoretical Probability, 22
P. Patie (2009)
A few remarks on the supremum of stable processesStatistics & Probability Letters, 79
J. Picard (2007)
Lévy Processes Conditioned to Stay Positive
(1970)
Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
(2007)
Table of Integrals, Series and Products
J. Bertoin, M. Yor (2005)
Exponential functionals of Levy processesProbability Surveys, 2
Violetta Bernyk, R. Dalang, G. Peskir (2007)
The law of the supremum of a stable Lévy process with no negative jumpsAnnals of Applied Probability, 36
A. Kyprianou, Juan Pardo, V. Rivero (2008)
Exact and asymptotic n-tuple laws at first and last passageAnnals of Applied Probability, 20
P. Patie (2009)
Law of the absorption time of some positive self-similar Markov processesAnnals of Probability, 40
R. Getoor (1979)
The Brownian Escape ProcessAnnals of Probability, 7
BY Chaumont, L. Chaumont (2013)
ON THE LAW OF THE SUPREMUM OF LÉVY PROCESSES 1
J. Billingham, A. King (1997)
Uniform asymptotic expansions for the Barnes double gamma functionProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 453
Ning Cai, S. Kou (2012)
Pricing Asian Options Under a Hyper-Exponential Jump Diffusion ModelOper. Res., 60
G. Pólya, G. Szegö (1998)
Functions of One Complex Variable
E. Barnes
The theory of the double gamma functionProceedings of the Royal Society of London, 66
M.E. Caballero, J.C. Pardo, J.L. Pérez (2010)
On Lamperti stable processesProbab. Math. Stat., 30
L. Chaumont, J.C. Pardo (2006)
The lower envelope of positive self-similar Markov processesElectron. J. Probab., 11
Juan Millan (2006)
On the future infimum of positive self-similar Markov processesStochastics, 78
L. Chaumont, A. Kyprianou, Juan Millan (2007)
Some explicit identities associated with positive self-similar Markov processes.Stochastic Processes and their Applications, 119
V. Rivero (2003)
A law of iterated logarithm for increasing self-similar Markov processesStochastics and Stochastic Reports, 75
佐藤 健一 (2013)
Lévy processes and infinitely divisible distributions
M. Caballero, Juan Pardo, José Pérez (2008)
On the Lamperti stable processesarXiv: Probability
A. Kuznetsov (2010)
On extrema of stable processes.Annals of Probability, 39
Bénédicte Haas (2003)
Loss of mass in deterministic and random fragmentationsStochastic Processes and their Applications, 106
L. Chaumont (1996)
Conditionings and path decompositions for Lévy processesStochastic Processes and their Applications, 64
E.W. Barnes (1901)
The theory of the double gamma functionPhilos. Trans. R. Soc. Lond. A, 196
R. Doney (1987)
On Wiener-Hopf Factorisation and the Distribution of Extrema for Certain Stable ProcessesAnnals of Probability, 15
J. Bertoin, M. Yor (2002)
The Entrance Laws of Self-Similar Markov Processes and Exponential Functionals of Lévy ProcessesPotential Analysis, 17
A. Kyprianou (2006)
Introductory Lectures on Fluctuations of Lévy Processes with Applications
A. Kyprianou, Juan Pardo (2008)
Continuous-State Branching Processes and Self-SimilarityJournal of Applied Probability, 45
(2009)
Exponential functionals of a new family of Lévy processes and self-similar continuous state branching processes with immigration
M. Abramowitz, I. Stegun, David Miller (1965)
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Journal of Applied Mechanics, 32
V. Mercado (2007)
Recurrent extensions of self-similar Markov processes and Cramer's condition
A. Kuznetsov, A. Kyprianou, J. Pardo, K. Schaik (2009)
A Wiener–Hopf Monte Carlo simulation technique for Lévy processesAnnals of Applied Probability, 21
M. Caballero, J. Pardo, J. Pérez (2009)
Explicit identities for Lévy processes associated to symmetric stable processesBernoulli, 17
Vincent Vigon (2002)
Simplifiez vos Lévy en titillant la factorisation de Wierner-Hopf
Krishanu Maulik, B. Zwart (2006)
Tail asymptotics for exponential function-als of L evy processes
We study the distribution and various properties of exponential functionals of hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained in Hubalek and Kuznetsov (Electron. Commun. Probab. 16:84–95, 2011) and Kuznetsov (Ann. Probab. 39(3):1027–1060, 2011). We also derive several new results related to (i) the entrance law of a stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of a stable process reflected at its past infimum, (iii) the distribution of the lifetime of a stable process conditioned to hit zero continuously and (iv) the entrance law and the last passage time of the radial part of a multidimensional symmetric stable process.
Acta Applicandae Mathematicae – Springer Journals
Published: May 10, 2012
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