Open AccessBook
Lévy processes and infinitely divisible distributions
Reads0
Chats0
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
The Hausdorff Dimension of Operator Semistable Lévy Processes
Peter Kern,Lina Wedrich +1 more
TL;DR: Meerschaert and Xiao as discussed by the authors considered the special case of an operator stable (selfsimilar) Levy process and determined the Hausdorff dimension of the partial range X(B) in terms of the real parts of the eigenvalues of E.
Journal ArticleDOI
On the likelihood function of small time variance Gamma Lévy processes
TL;DR: In this article, the likelihood function of small generalized Laplace laws and variance gamma Levy processes in the short time framework was investigated and the local asymptotic normality property in statistical inference for the variance gamma gamma Levy process under high-frequency sampling with its associated optimal convergence rate and Fisher information matrix.
Journal ArticleDOI
Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps
Guodong Pang,Nikola Sandrić +1 more
TL;DR: In this paper, the long-time behavior of a particle immersed in a turbulent environment driven by a diusion with jumps was studied, and the law of large numbers and central limit theorem for the evolution process of the tracked particle was derived.
Journal ArticleDOI
hp-DGFEM FOR KOLMOGOROV–FOKKER–PLANCK EQUATIONS OF MULTIVARIATE LÉVY PROCESSES
TL;DR: In this paper, the authors analyze the discretization of nonlocal degenerate integrodifferential equations arising as so-called forward equations for jump-diffusion processes in option pricing problems.
Posted Content
Classes of infinitely divisible distributions on R^d related to the class of selfdecomposable distributions
TL;DR: In this paper, the authors studied new classes of infinitely divisible distributions on R^d and characterized the nested subclasses of those classes by stochastic integral representations and another is in terms of Levy measures.
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.