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Lévy processes and infinitely divisible distributions
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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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Implicit renewal theory for exponential functionals of L\'evy processes
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TL;DR: In this paper, a new functional relation for the probability density function of the exponential functional of a Levy process is established, which allows to significantly simplify the techniques commonly used in the study of these random variables and hence provide quick proofs of known results, derive new results, as well as sharpening known estimates for the distribution.
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An Lq(Lp)-theory for diffusion equations with space-time nonlocal operators
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Invariant manifolds with boundary for jump-diffusions
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Heat content for convolution semigroups
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TL;DR: In this paper, the authors studied the asymptotic behavior of isotropic Levy processes under mild assumptions on the characteristic exponent and treated the class of Levy processes with finite variation in full generality.
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Continuity Correction for Barrier Options in Jump-Diffusion Models
El Hadj Aly Dia,Damien Lamberton +1 more
TL;DR: The aim of this paper is to study the continuity correction for barrier options in jump-diffusion models by expressing the payoff of a barrier option in terms of the maximum of the underlying process.
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.