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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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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.
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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.
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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.
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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.
References
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Journal ArticleDOI
Explicit formula for the supremum distribution of a spectrally negative stable process
TL;DR: In this paper, a generalization of the well-known formula for the supremum distribution of Wiener process with infinite variation has been derived for a spectrally positive or negative Levy process.
Journal ArticleDOI
A Multivariate Functional Limit Theorem in Weak $$M_{1}$$ Topology
Bojan Basrak,Danijel Krizmanić +1 more
TL;DR: In this article, a functional limit theorem for weakly dependent regularly varying sequences of random vectors was proved for the case where the convergence takes place in the space of valued cadlag functions endowed with the so-called weak $$M_1}$$ topology.
Journal ArticleDOI
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.
Journal ArticleDOI
On infinitely divisible distributions with polynomially decaying characteristic functions
TL;DR: In this article, necessary and sufficient conditions on the characteristics of an infinitely divisible distribution under which its characteristic function φ decays polynomially were provided. And they showed that under a mild regularity condition this polynomial decay is equivalent to 1 / φ being a Fourier multiplier on Besov spaces.
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.