scholarly journals Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes

Bernoulli ◽  
2007 ◽  
Vol 13 (1) ◽  
pp. 195-210 ◽  
Author(s):  
Serge Cohen ◽  
Jan Rosinski
Keyword(s):  
Lévy Processes ◽  
Gaussian Approximation ◽  
Levy Processes ◽  
Stable Processes

scholarly journals Oscillation of modes of some semi-stable Lévy processes

1993 ◽  
Vol 132 ◽  
pp. 141-153 ◽  
Author(s):  
Toshiro Watanabe
Keyword(s):  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Stable Processes ◽  
Unimodal Lévy Process ◽  
Oscillating Mode

In this paper it is shown that there is a unimodal Levy process with oscillating mode. After the author first constructed an example of such a self-decomposable process, Sato pointed out that it belongs to the class of semi-stable processes with β < 0. We prove that all non-symmetric semi-stable self-decomposable processes with β < 0 have oscillating modes.

scholarly journals The Entrance Law of the Excursion Measure of the Reflected Process for Some Classes of Lévy Processes

2019 ◽  
Vol 169 (1) ◽  
pp. 59-77
Author(s):  
Loïc Chaumont ◽  
Jacek Małecki
Keyword(s):  
Lévy Processes ◽  
Characteristic Exponent ◽  
Levy Processes ◽  
Time Variable ◽  
Stable Processes ◽  
The Laplace Transform ◽  
Entrance Law ◽  
Generalized Eigenfunctions ◽  
Positive Half ◽  
Integral Formulae

Abstract We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric Lévy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the density of the entrance law in terms of the generalized eigenfunctions for the semigroup of the process killed when exiting the positive half-line. We use the formulae to study in-depth properties of the density of the entrance law such as asymptotic behavior of its derivatives in time variable.

scholarly journals Double hypergeometric Lévy processes and self-similarity

2021 ◽  
Vol 58 (1) ◽  
pp. 254-273
Author(s):  
Andreas E. Kyprianou ◽  
Juan Carlos Pardo ◽  
Matija Vidmar
Keyword(s):  
Closed Form ◽  
Markov Processes ◽  
Lévy Processes ◽  
Levy Processes ◽  
Stable Processes ◽  
Self Similarity ◽  
New Family ◽  
Self Similar

AbstractMotivated by a recent paper (Budd (2018)), where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Lévy processes, called the double hypergeometric class, whose Wiener–Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.

scholarly journals A Gaussian approximation theorem for Lévy processes

2021 ◽  
pp. 109187
Author(s):  
David Bang ◽  
Jorge González Cázares ◽  
Aleksandar Mijatović
Keyword(s):  
Lévy Processes ◽  
Approximation Theorem ◽  
Gaussian Approximation ◽  
Levy Processes

scholarly journals Explicit identities for Lévy processes associated to symmetric stable processes

Bernoulli ◽  
2011 ◽  
Vol 17 (1) ◽  
pp. 34-59 ◽  
Author(s):  
M.E. Caballero ◽  
J.C. Pardo ◽  
J.L. Pérez
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Stable Processes ◽  
Symmetric Stable Processes

scholarly journals The extended hypergeometric class of Lévy processes

2014 ◽  
Vol 51 (A) ◽  
pp. 391-408 ◽  
Author(s):  
A. E. Kyprianou ◽  
J. C. Pardo ◽  
A. R. Watson
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Stable Processes ◽  
Exponential Functional ◽  
Extended Class

We review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (2013) with a view to computing fluctuation identities related to stable processes. We give the Wiener-Hopf factorisation of a process in the extended class, characterise its exponential functional, and give three concrete examples arising from transformations of stable processes.

scholarly journals More on hypergeometric Lévy processes

2016 ◽  
Vol 48 (A) ◽  
pp. 153-158
Author(s):  
Emma L. Horton ◽  
Andreas E. Kyprianou
Keyword(s):  
Lévy Processes ◽  
Characteristic Exponent ◽  
Levy Processes ◽  
Stable Processes ◽  
Short Article ◽  
The Family ◽  
Self Similar ◽  
Definition Of ◽  
Complex Valued ◽  
Independent Parameters

AbstractKuznetsov and co-authors in 2011‒14 introduced the family of hypergeometric Lévy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of positive self-similar Markov processes. Hypergeometric Lévy processes are defined through their characteristic exponent, which, as a complex-valued function, has four independent parameters. In 2014 it was shown that the definition of a hypergeometric Lévy process could be taken to include a greater range of the aforesaid parameters than originally specified. In this short article, we push the parameter range even further.

scholarly journals Tanaka formula for strictly stable processes

2019 ◽  
Vol 39 (1) ◽  
pp. 39-60
Author(s):  
Hiroshi Tsukada
Keyword(s):  
Potential Theory ◽  
Lévy Processes ◽  
Levy Processes ◽  
Stochastic Calculus ◽  
Local Times ◽  
Stable Processes ◽  
Tanaka Formula

For symmetric Levy processes, if the local times exist, the Tanaka formula has already been constructed via the techniques in the potential theory by Salminen and Yor 2007. In this paper, we study the Tanaka formula for arbitrary strictly stable processes with index α ∈ 1, 2, including spectrally positive and negative cases in a framework of Ito’s stochastic calculus. Our approach to the existence of local times for such processes is different from that of Bertoin 1996.

Sign in / Sign up

Export Citation Format

Share Document