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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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Global solutions to stochastic Volterra equations driven by Lévy noise
Erika Hausenblas,Mihály Kovács +1 more
TL;DR: In this paper, the existence and uniqueness of semilinear stochastic Volterra equations driven by multiplicative Levy noise of pure jump type was investigated and conditions on b, F G and GL under which a unique global solution exists.
Book ChapterDOI
A Dynamic Lévy Copula Model for the Spark Spread
TL;DR: In this article, the authors present a model for the spark spread on energy markets, which is implied by a two-dimensional model for electricity and gas spot prices, and employ Fourier transform techniques to derive semi-analytic expressions for option prices.
Journal ArticleDOI
Efficient simulation of Lévy-driven point processes
TL;DR: In this article, the authors introduce a new large family of Levy-driven point processes with (and without) contagion, by generalising the classical self-exciting Hawkes process and doubly stochastic Poisson processes with non-Gaussian Levy-based Ornstein-Uhlenbeck-type intensities.
Numerical Approximation of Stochastic Differential Equations Driven by Levy Motion with Infinitely Many Jumps
TL;DR: In this paper, the authors consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity, and provide a good approximation method for the original stochiastic differential equation that can also be implemented numerically.
Posted Content
Convolution inequalities for Besov and Triebel--Lizorkin spaces, and applications to convolution semigroups
Franziska Kühn,René L. Schilling +1 more
TL;DR: In this paper, the authors study the mapping properties of convolution semigroups, considered as operators on the function spaces $A_{p,q}^s, $A \in \{B,F\}$.
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.