The theory of scale functions for spectrally negative Lévy processes
The purpose of this review article is to give an up to date account of the theory and
applications of scale functions for spectrally negative Lévy processes. Our review also …
applications of scale functions for spectrally negative Lévy processes. Our review also …
[图书][B] Fluctuations of Lévy processes with applications: Introductory Lectures
AE Kyprianou - 2014 - books.google.com
Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …
class of stochastic processes around which a robust mathematical theory exists. Their …
[图书][B] Introductory lectures on fluctuations of Lévy processes with applications
AE Kyprianou - 2006 - books.google.com
Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …
class of stochastic processes around which a robust mathematical theory exists. Their …
Old and new examples of scale functions for spectrally negative Lévy processes
F Hubalek, E Kyprianou - Seminar on Stochastic Analysis, Random Fields …, 2011 - Springer
We give a review of the state of the art with regard to the theory of scale functions for
spectrally negative Lévy processes. From this we introduce a general method for generating …
spectrally negative Lévy processes. From this we introduce a general method for generating …
[PDF][PDF] Stable Lévy processes, self-similarity and the unit ball.
AE Kyprianou - ALEA. Latin American Journal of Probability & …, 2018 - warwick.ac.uk
Around the 1960s a celebrated collection of papers emerged offering a number of explicit
identities for the class of isotropic Lévy stable processes in one and higher dimensions; …
identities for the class of isotropic Lévy stable processes in one and higher dimensions; …
Meromorphic Lévy processes and their fluctuation identities
The last couple of years has seen a remarkable number of new, explicit examples of the
Wiener–Hopf factorization for Lévy processes where previously there had been very few. We …
Wiener–Hopf factorization for Lévy processes where previously there had been very few. We …
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes
A Kuznetsov - 2010 - projecteuclid.org
In this paper we introduce a ten-parameter family of Lévy processes for which we obtain
Wiener–Hopf factors and distribution of the supremum process in semi-explicit form. This …
Wiener–Hopf factors and distribution of the supremum process in semi-explicit form. This …
Martingales in self-similar growth-fragmentations and their connections with random planar maps
The purpose of the present work is twofold. First, we develop the theory of general self-
similar growth-fragmentation processes by focusing on martingales which appear naturally …
similar growth-fragmentation processes by focusing on martingales which appear naturally …
Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes
A Kuznetsov, JC Pardo - Acta Applicandae Mathematicae, 2013 - Springer
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 …
hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the …
A note on scale functions and the time value of ruin for Lévy insurance risk processes
E Biffis, AE Kyprianou - Insurance: Mathematics and Economics, 2010 - Elsevier
We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally
negative Lévy process; the natural class of stochastic processes which contains many …
negative Lévy process; the natural class of stochastic processes which contains many …