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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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A new family of tempered distributions
TL;DR: Tempered distributions have received considerable attention, both from a theoretical point of view and in several important application fields as mentioned in this paper, and the most popular choice is perhaps the Tweedie model, which is obtained by tempering the Positive Stable distribution.
Journal ArticleDOI
Pricing Covariance Swaps for Barndorff-Nielsen and Shephard Process Driven Financial Markets
TL;DR: In this paper, the authors studied the arbitrage free pricing of the covariance swap for Barndorff-Nielsen and Shephard type L\'evy process driven financial markets.
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The set-indexed Lévy process: Stationarity, Markov and sample paths properties
Erick Herbin,Ely Merzbach +1 more
TL;DR: In this article, a satisfactory definition of the important class of Levy processes indexed by a general collection of sets is presented, and a new definition for increment stationarity of set-indexed processes is used to obtain different characterizations of this class.
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A Note on Malliavin Fractional Smoothness for Lévy Processes and Approximation
TL;DR: In this paper, the authors investigated the behavior of L 2-martingale Levy processes for certain integrands φ and showed that fractional smoothness depends on the distribution of the Levy process.
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Stable cylindrical Lévy processes and the stochastic Cauchy problem
TL;DR: In this paper, the authors consider the stochastic Cauchy problem driven by the canonical α-stable cylindrical Levy process and derive a sufficient and necessary condition for the existence of the weak and mild solution.
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.