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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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Natural metrics and least-committed priors for articulated tracking
TL;DR: This work introduces the spatial kinematic manifold of joint positions, which is embedded in a high dimensional Euclidean space, and develops a least-committed Brownian motion model on the manifold that respects the natural metric.
Journal ArticleDOI
Multilevel Monte Carlo for L\'evy-driven SDEs: Central limit theorems for adaptive Euler schemes
Steffen Dereich,Sangmeng Li +1 more
TL;DR: In this article, the authors consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by Levy processes and prove stable convergence of an idealised scheme.
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Asymptotic behaviour of first passage time distributions for Lévy processes
Ron Doney,Victor Rivero +1 more
TL;DR: In this article, the authors studied the local behavior of the distribution of the lifetime under the characteristic measure of excursions away from the point of origin of the process, reflected in its past infimum.
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Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function
TL;DR: Goodness-of-fit testing for multivariate stable distributions is considered and the proposed test statistics exploit a characterizing property of the characteristic function of these distributions and are consistent under some conditions.
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Weak subordination of multivariate Lévy processes and variance generalised gamma convolutions
TL;DR: In this paper, the variance generalised gamma convolution class of Levy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination, which is an extension of both univariate and multivariate subordination.
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.