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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
Citations
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Compound random measures and their use in Bayesian non-parametrics
Jim E. Griffin,Fabrizio Leisen +1 more
TL;DR: In this paper, a new class of dependent random measures called compound random measures is proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered.
Posted Content
Introductory Lectures on Stochastic Population Systems
TL;DR: A review of basic stochastic population models including branching processes and models of population genetics can be found in this paper, where some basic methods for their analysis are also introduced together with some basic metrics.
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Sparse Stochastic Processes and Discretization of Linear Inverse Problems
TL;DR: A novel statistically-based discretization paradigm is presented and a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems are derived, guided by the theory of sparse stochastic processes.
Journal ArticleDOI
Time-changed Poisson processes
TL;DR: In this article, the authors considered time-changed Poisson processes and derived the governing difference-differential equations (DDEs) for these processes, and derived a new governing partial differential equation for the tempered stable subordinator of index 0 β 1.
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Approximation properties for solutions to non-Lipschitz stochastic differential equations with Lévy noise
TL;DR: In this paper, the authors considered non-Lipschitz stochastic differential equations with delays driven by Levy noise, and the approximation theorems for the solutions to these two kinds of equations were proposed respectively.
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.