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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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Journal ArticleDOI
Global properties of stochastic Loewner evolution driven by Lévy processes
TL;DR: In this article, a generalized SLE driven by a superposition of a Brownian motion and a fractal set of jumps (technically a stable Levy process) is studied.
Journal ArticleDOI
On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data
TL;DR: This work considers uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the model order is assumed to be known and necessary and sufficient conditions for uniqueness of general AR models are provided.
Journal ArticleDOI
Robust Option Pricing with Characteristic Functions and the B-Spline Order of Density Projection
TL;DR: In this paper, the authors extend and refine the method of option pricing by frame projection of risk-neutral densities to incorporate general B-splines, including the cubic basis, and general payoff structures.
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Volatility occupation times
TL;DR: In this paper, nonparametric estimators of the occupation measure and the occupation density of the stochastic volatility of a discretely observed Ito semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically.
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On discrete-time semi-Markov processes
TL;DR: In this paper, a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and the related governing convolution type equations are obtained.
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.