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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
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Option Calibration of Exponential Lévy Models: Confidence Intervals and Empirical Results
Jakob Söhl,Mathias Trabs +1 more
TL;DR: In this paper, the authors propose a nonparametric spectral estimation procedure for finite and infinite jump activity based on options on the German DAX index and find that both methods achieve good calibration results.
Dissertation
Higher-order airy functions of the first kind and spectral properties of the massless relativistic quartic anharmonic oscillator
TL;DR: In this article, a class of special functions Aik (y), k = 2, 4, 6, · · ·, generalising the classical Airy function Ai(y) to higher orders was studied.
Journal ArticleDOI
Estimation and simulation for multivariate tempered stable distributions
Yunfei Xia,Michael Grabchak +1 more
TL;DR: In this paper, a methodology for the simulation and parameter estimation of multivariate tempered stable distributions with an emphasis on the bivariate case is introduced, based on an approximatio...
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Multivariate generalized Ornstein–Uhlenbeck processes
Anita Behme,Alexander Lindner +1 more
TL;DR: In this paper, a multivariate generalized Ornstein-Uhlenbeck (MGOU) process is defined, which is characterized by a starting random variable and some Levy process (X, Y ) in R m × m × R m.
Book ChapterDOI
Nonlocal Transport Theories in Geomorphology: Mathematical Modeling of Broad Scales of Motion
TL;DR: Nonlocal constitutive laws as mentioned in this paper are a subclass of geomorphic transport laws, in which the flux at a point depends on the conditions in some larger neighborhood around this point in space and/or in time.
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.