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
Journal ArticleDOI
Efficient nonparametric inference for discretely observed compound Poisson processes
TL;DR: In this paper, a compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times, and nonparametric estimators of the jump and Levy distributions are proposed and functional central limit theorems using the uniform norm are proved for both under mild conditions.
Posted Content
High-order short-time expansions for ATM option prices under the CGMY model
TL;DR: In this article, a second-order approximation for ATM option prices under the CGMY L evy model is derived and, then, extended to a model with an additional independent Brownian component.
Journal ArticleDOI
Stochastic equations of super-Lévy processes with general branching mechanism☆
Hui He,Zenghu Li,Xu Yang +2 more
TL;DR: In this article, the process of distribution functions of a one-dimensional super-Levy process with general branching mechanism is characterized as the pathwise unique solution of a stochastic integral equation driven by time-space Gaussian white noises and Poisson random measures.
Posted Content
Perpetual Options for L evy Processes in the Bachelier Model
Ernesto Mordecki,Centro de Matem +1 more
TL;DR: In this paper, a solution to the optimal stopping problem is given, where X =fXtgt 0 is a L evy process, is an arbitrary stopping time, 0 is the discount rate, and the reward function g takes the form gc(x) = (x K) + orgp(x), = (K x + X ) + results, interpreted as option prices of perpetual options in Bachelier's model, are expressed in terms of the distribution of the overall supremum in case g = gc and overall inmum, in case
Journal ArticleDOI
A Lévy Based Approach to Random Vector Fields: With a View Towards Turbulence
Emil Hedevang,Jürgen Schmiegel +1 more
TL;DR: In this paper, the Shkarofsky correlation family was used to model the small-scale behavior of fully developed turbulence in the boundary layer of the wind energy industry. But, the authors only considered the energy spectrum of the Lévy base.
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.