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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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Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem
TL;DR: In this paper, the covariance function of an isotropic Gaussian stochastic field on the unit sphere is estimated using a single observation at each point of the discretized sphere.
Tail behavior of multivariate levy-driven mixed moving average processes and supou
Martin Moser,Robert Stelzer +1 more
TL;DR: In this article, the authors introduce multivariate Levy-driven mixed moving average (MMA) processes and give conditions for their existence and regular variation of the stationary distributions, and study the tail behavior of multivariate supOU processes and of a stochastic volatility model, where a positive semidefinite supOU process models the volatility.
Journal ArticleDOI
Instantaneous Portfolio Theory
TL;DR: In this article, the univariate variance gamma model is extended to higher dimensions with an arrival rate function with full support in high dimensions and independent levels of skewness and excess kurtosis across assets.
Journal ArticleDOI
Time series regression on integrated continuous-time processes with heavy and light tails
TL;DR: In this paper, a multivariate Ornstein-Uhlenbeck process with an additional noise term is used to model the linear combinations of Brownian motions and stable Levy processes, whose characteristic triplets have an explicit analytic representation.
Posted Content
On the spectral vanishing viscosity method for periodic fractional conservation laws
Simone Cifani,Espen R. Jakobsen +1 more
TL;DR: It is proved that this spectral vanishing viscosity approximation of periodic fractional conservation laws converges to the entropy solution of the problem, retains the spectral accuracy of the Fourier method, and diagonalizes the fractional term reducing dramatically the computational cost induced by this term.
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.