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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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Journal ArticleDOI
Sieve-based confidence intervals and bands for L\'{e}vy densities
TL;DR: In this paper, central limit theorems for these sieve estimators, both pointwise and uniform on an interval away from the origin, are obtained, leading to pointwise confidence intervals and bands for the L\'{e}vy density.
Journal ArticleDOI
Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues
TL;DR: In this article, the authors studied the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or asymptotically negligible service interruptions in the Halfin-Whitt regime as special cases.
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Extension and trace for nonlocal operators
TL;DR: In this paper, an optimal extension and trace theorem for Sobolev spaces of nonlocal operators is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem.
Posted Content
Estimates of heat kernels of non-symmetric L\'evy processes
TL;DR: In this article, the densities of non-symmetric Levy processes were investigated and upper and lower estimates of the density and its derivatives were derived for the case when the corresponding jump measure is allowed to be highly non-Symmetric and the characteristic exponent satisfies a scaling condition.
Posted Content
Levy Based Cross-Commodity Models and Derivative Valuation
TL;DR: A new cross-commodity modeling framework which accounts for jumps and cointegration in prices and introduces a new derivative valuation methodology by working in Fourier space, tailored for mean-reverting models.
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.