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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
Citations
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On the exponential moments of additive processes with the structure of semimartingales
TL;DR: In this article, the exponential moments of R-valued additive processes with the strucure of semimartingales, which are regarded as the Laplace transforms of the laws of these additive processes, are explicitly represented by their characteristics.
On Pathwise Stochastic Integration of Processes with Unbounded Power Variation
TL;DR: In this paper, a class of stochastic processes which can be represented as a composition of a Holder continuous process with a non-random function of locally bounded variation is studied, and new conditions are presented for the existence of generalized Lebesgue-Stieltjes integrals for these processes with respect to general Holder continuous processes.
Posted Content
The maximal jump and local convergence of continuous-state branching processes
TL;DR: In this article, the distribution of the maximal jump of continuous state branching processes is studied and exact expressions and explicit asymptotics of both the local maximal jump and the global maximal jump are obtained.
Journal ArticleDOI
Slow manifolds for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise
TL;DR: In this paper, the slow dynamics of a non-local fast-slow stochastic evolutionary system with stable Levy noise were investigated. And two examples with numerical simulations are presented to illustrate the results.
Proceedings Article
Generalization bound for infinitely divisible empirical process
Chao Zhang,Dacheng Tao +1 more
TL;DR: This paper develops deviation inequalities for the sequence of random variables of an ID distribution and shows the generalization bound for ID empirical process based on the annealed VapnikChervonenkis (VC) entropy, according to Sauer's lemma.
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.