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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
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Exponential ergodicity and regularity for equations with L\'evy noise
TL;DR: In this paper, the authors prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by $\alpha$-stable noises in finite and in infinite dimensions.
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Adaptive estimation of continuous-time regression models using high-frequency data
TL;DR: In this article, the authors derived the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous-time regression model for the continuous martingale parts of two Ito semimartingales observed on a fixed time interval.
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On the Novikov-Shiryaev Optimal Stopping Problems in Continuous Time
TL;DR: Novikov and Shiryaev as discussed by the authors gave explicit solutions to a class of optimal stopping problems for random walks based on other similar examples given in Darling et al. (1972) and gave the analogue of their results when the random walk is replaced by a Levy process.
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On the limit distributions of continuous-state branching processes with immigration
TL;DR: In this article, the authors considered the class of continuous state branching processes with immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) and their limit distributions as time tends to infinity.
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Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models
TL;DR: In this paper, the authors consider several time-varying volatility and/or heavy-tailed models to explain the dynamics of return time series and to fit the volatility smile for exchange-traded options where the underlying is the main Borsa Italiana stock index.
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.