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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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Heat kernel estimates for symmetric jump processes with mixed polynomial growths
TL;DR: In this paper, the transition densities of pure-jump symmetric Markov processes with mixed polynomial growth were studied. And they were shown to be equivalent to the Khintchine-type law of iterated logarithm at the infinity.
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On the roughness of the paths of RBM in a wedge
TL;DR: In this paper, it was shown that on excursion intervals of Z away from the origin, (Z,Y ) satisfies the standard Skorokhod problem for X, but not on the entire time horizon.
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Spectral Heat Content for L\'evy Processes
TL;DR: In this article, the spectral heat content for L'evy processes of bounded variation was studied and the asymptotic behavior of the heat content was shown to be stable under integrable perturbations to the L 'evy measure.
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Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes∗
Yuji Umezawa,Akira Yamazaki +1 more
TL;DR: In this paper, a backward recurrence relation for computing multivariate characteristic functions of the intertemporal joint distribution of time-changed Levy processes is derived for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a timechanged Levy process.
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Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: Solution, stochastic paths, and applications.
TL;DR: This paper studies the subdiffusion-limited model, which is defined by mesoscopic equations with fractional derivatives applied to both the movement and the reaction terms, and identifies some precise microscopic conditions that dictate when this type of mesoscopic model is or is not appropriate.
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.