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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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Fluctuations of Lévy Processes with Applications
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Ten equivalent definitions of the fractional laplace operator
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Optimal stopping and perpetual options for Lévy processes
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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.
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A general approach to approximation theory of operator semigroups
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Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion
TL;DR: In this article, a product of a symmetric stable process and a one-dimensional Brownian motion is considered, and bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally Holder continuous.
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Some Considerations on the Structure of Transition Densities of Symmetric Levy Processes
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Recent Developments in Financial and Insurance Mathematics and the Interplay with the Industry
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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.