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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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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.
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.
Journal ArticleDOI
Density and tails of unimodal convolution semigroups
TL;DR: For the isotropic unimodal probability convolutional semigroups, this article gave sharp bounds for their Levy-Khintchine exponent with Matuszewska indices strictly between 0 and 2.
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.
References
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Journal ArticleDOI
Occupation Time Fluctuations of Weakly Degenerate Branching Systems
Yuqiang Li,Yimin Xiao +1 more
TL;DR: In this paper, the authors established limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems with anisotropic space motion and weakly degenerate splitting ability.
Book ChapterDOI
Levy Preservation and Associated Properties for f -Divergence Minimal Equivalent Martingale Measures
TL;DR: In this paper, the authors studied the properties of f-divergence minimal martingale measures and gave necessary and sufficient conditions for existence of such measures, including scaling and invariance in time properties.
Posted Content
Mixed Tempered Stable distribution
Edit Rroji,Lorenzo Mercuri +1 more
TL;DR: The Mixed Tempered Stable (MTS) distribution as discussed by the authors is a parametric distribution with the same structure of the Normal Variance Mean Mixtures (NVM) but the normality assumption leaves place to a semi-heavy tailed distribution.
Journal ArticleDOI
On the convergence of quadratic variation for compound fractional Poisson processes
Enrico Scalas,Noèlia Viles +1 more
TL;DR: In this paper, the convergence of quadratic variation for compound renewal processes and M-Wright functions is investigated both as a random variable (for given t) and as a stochastic process.
Journal ArticleDOI
Kanter random variable and positive free stable distributions
TL;DR: In this article, the density of some power of a positive stable distribution is a completely monotone function and the distribution function of the latter variable is written down and gives a more explicit description of the non commutative analogue of positive stable distributions in the setting of Voiculescu's free probability theory.