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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
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Journal ArticleDOI
Tempered stable distributions and processes
Uwe Küchler,Stefan Tappe +1 more
TL;DR: In this paper, the authors investigate the class of tempered stable distributions and their associated processes, including limit distributions, parameter estimation and the study of their densities, and deal with density transformations and compute their p -variation indices.
Journal ArticleDOI
Density Approximations for Multivariate Affine Jump-Diffusion Processes
TL;DR: In this article, the authors introduce closed-form transition density expansions for multivariate affine jump-diffusion processes, which rely on a general approximation theory which is developed in weighted Hilbert spaces for random variables which possess all polynomial moments.
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Estimates of transition densities and their derivatives for jump Lévy processes
TL;DR: In this paper, upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy-Khinchin exponent are given.
Posted Content
Aggregation in Large Dynamic Panels
TL;DR: In this article, the authors considered the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross-sectionally dependent.
Journal ArticleDOI
Properties and numerical evaluation of the Rosenblatt distribution
Mark S. Veillette,Murad S. Taqqu +1 more
TL;DR: In this article, a technique for computing the cumulants of the Rosenblatt distribution is described and the coefficients of this expansion are derived using the L\'{e}vy-Khintchine formula.
References
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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.