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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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Journal ArticleDOI
Some Considerations on the Structure of Transition Densities of Symmetric Levy Processes
TL;DR: For a class of symmetric Lévy processes (Yt)t = e − 1 t /p 1 t (0), t > 0, it was shown in this article that the transition density πt,0 of PXt−X0 is controlled by δψ, 1 t and d ψ,1 t with δ ψ 1 t controlling π t,0(0) and dψ, 1 t the spatial decay.
Journal ArticleDOI
Recent Developments in Financial and Insurance Mathematics and the Interplay with the Industry
TL;DR: Asmussen et al. as mentioned in this paper presented a multivariate random walk with regularly varying step sizes to solve high-dimensional singular control problems in finance and insurance, and the results showed that the approach can be used to solve problems in both finance and actuarial mathematics.
Journal ArticleDOI
Wave Decoherence for the Random Schrödinger Equation with Long-Range Correlations
TL;DR: In this paper, the authors studied the loss of coherence of a wave propagating according to the Schrodinger equation with a time-dependent random potential, where the random potential is assumed to have slowly decaying correlations.
Posted Content
Symmetric Rearrangements Around Infinity with Applications to Levy Processes
TL;DR: In this article, a rearrangement inequality for multiple integrals is proposed, which partially generalizes a result of Friedberg and Luttinger (1976) and can be interpreted as involving symmetric rearrangements of domains around infinity.
Book
Recent progress in theory and applications : fractional Lévy fields, and scale functions
TL;DR: The theory of scale functions for Spectrally Negative Levy Processes has been studied in this article for fractional Levy Fields, where the scale function is defined as a scale function for the fractional field.
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.