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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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Affine processes beyond stochastic continuity
TL;DR: In this paper, a general theory of finite dimensional affine semimartingales under very weak assumptions is developed and affine Markov processes have affine form and the conditional characteristic function can be represented with solutions to measure differential equations of Riccati type.
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Shot-noise driven multivariate default models
TL;DR: In this paper, a multivariate default model with interesting stylized properties is introduced in the following way: a non-decreasing shot-noise process serves as common stochastic clock.
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On subordinate random walks
TL;DR: In this article, it was shown that a scaled subordination of a random walk converges to a multiple of a rotationally stable process if and only if the Laplace exponent of the corresponding subordinator varies regularly at zero.
Posted Content
On representation theorem of sublinear expectation related to G-L\'evy process and paths of G-L\'evy process
TL;DR: In this article, the representation of an important sublinear expectation under which a new stochastic process G-L\'evy process has been introduced is studied. And the existence of a weakly compact family of probability measures to give the representation by using two different methods.
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The Wiener condition and the conjectures of Embrechts and Goldie
TL;DR: In this article, it was shown that the class of convolution equivalent distributions and locally subexponential distributions are not closed under convolution roots, which is a negative answer to the classical conjectures of Embrechts and Goldie.
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.