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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
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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.
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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.
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Entrance laws for positive self-similar Markov processes
TL;DR: In this article, the authors proposed an alternative approach to obtain the self-similar entrance laws for positive selfsimilar Markov processes, which can be embedded into a single one. And they applied the same technique to construct the same entrance law for other types of selfsimilar processes.
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Unimodality for free multiplicative convolution with free normal distributions on the unit circle
Takahiro Hasebe,Yuki Ueda +1 more
TL;DR: In this article, the authors study unimodality for free multiplicative convolution with free normal distributions on the unit circle and give four results on unimodal for the case of poisson kernels.
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Nonparametric Bayesian inference for L\'evy subordinators
TL;DR: Given discrete time observations over a growing time interval, a nonparametric Bayesian approach to estimation of the L‐evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators is considered.
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Uniform Boundary Harnack Principle for Rotationally Symmetric Levy processes in General Open Sets
TL;DR: In this article, the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous L\'evy processes was proved.
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Quanto Implied Correlation in a Multi-Lévy Framework
TL;DR: In this article, the authors apply the multivariate construction for Levy processes introduced by Ballotta and Bonfiglioli (2014) to propose an integrated model for the joint dynamics of FX exchange rates and asset prices.