Open AccessBook
Lévy processes and infinitely divisible distributions
TLDR
In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.Abstract:
Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.read more
Citations
More filters
Posted Content
Weak Subordination of Multivariate L\'evy Processes
TL;DR: In this article, the Variance Gamma model is extended with weak subordination, which is an extension of both univariate and multivariate subordination and provides two applications: a weak formulation of Variance-alpha-Gamma process that exhibits a wider range of dependence than using traditional subordination.
Dissertation
Asymptotic properties of fragmentation processes
TL;DR: In this article, the authors study some asymptotic properties of fragmentation processes and prove certain strong laws of large numbers for self-similar fragmentations and deal with the existence and uniqueness of solutions of the one-sided FKPP travelling wave equation for homogenous fragmentation processes.
Journal ArticleDOI
Capturing Non-Exchangeable Dependence in Multivariate Loss Processes with Nested Archimedean Lévy Copulas
TL;DR: Inspired by ideas and techniques from the distributional copula literature, the procedure of nesting Archimedean Lévy copulas is investigated, and a detailed analysis of this construction is provided, and conditions under which valid multivariate (nested) Lé Ivy copulas are obtained.
Posted Content
Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps
TL;DR: In this paper, the concept of gauge and time symmetries for semimartingales on Lie groups is introduced, and Markovian and non-Markovian examples of gauge symmetric processes are provided.
Posted Content
Limit Theorems For Sequences of Tempered Stable and Related Distributions
Abstract: In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element in this class can be approximated by the distribution of a linear combination of elementary p-tempered {\alpha}-stable random variables.
References
More filters
BookDOI
Fluctuations of Lévy Processes with Applications
TL;DR: In this article, Kloeden, P., Ombach, J., Cyganowski, S., Kostrikin, A. J., Reddy, J.A., Pokrovskii, A., Shafarevich, I.A.
Journal ArticleDOI
Ten equivalent definitions of the fractional laplace operator
TL;DR: In this article, several definitions of the Riesz fractional Laplace operator in R^d have been studied, including singular integrals, semigroups of operators, Bochner's subordination, and harmonic extensions.
Book ChapterDOI
The Theory of Scale Functions for Spectrally Negative Lévy Processes
TL;DR: In this article, the authors give an up-to-date account of the theory and applications of scale functions for spectrally negative Levy processes, including the first extensive overview of how to work numerically with scale functions.
Journal ArticleDOI
Optimal stopping and perpetual options for Lévy processes
TL;DR: A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained.
Extreme Events: Dynamics, Statistics and Prediction
TL;DR: In this paper, the authors review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics.