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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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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.
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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.
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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.
References
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The hitting time of zero for a stable process
TL;DR: In this article, the first hitting time of a two-sided jumping Markov additive process in the Lamperti-Kiu representation has been studied for real-valued self-similar Markov processes.
Journal ArticleDOI
Ergodic properties of anomalous diffusion processes
TL;DR: In this article, the ergodic properties of some classes of anomalous diffusion processes were studied using a measure of dependence called the Correlation Cascade, which is a generalization of the classical Khinchin theorem.
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Harnack inequalities for subordinate Brownian motions
Ante Mimica,Panki Kim +1 more
TL;DR: In this article, the scale invariant Harnack inequality was proved for the subordinator in the case of the Laplace exponent of the corresponding subordinator, and new forms of asymptotical properties of the Levy and potential density of the sub-dominator near zero were given.
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Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of L\'{e}vy processes
Kamil Kaleta,József Lőrinczi +1 more
TL;DR: In this paper, the authors introduce a class of L\'{e}vy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential.
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Markovian bridges: Weak continuity and pathwise constructions
TL;DR: In this article, a weakly continuous Markovian bridge is constructed for self-similar Feller processes with continuous transition densities by weak convergence considerations, which is the only version of Markovians that admit a natural parameterization in terms of the state space of the process.