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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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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.
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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.
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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.
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Density and tails of unimodal convolution semigroups
TL;DR: For the isotropic unimodal probability convolutional semigroups, this article gave sharp bounds for their Levy-Khintchine exponent with Matuszewska indices strictly between 0 and 2.
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.
References
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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.
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Transition probabilities of Lévy‐type processes: Parametrix construction
TL;DR: In this article, the authors present an existence result for L\\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,xi) with respect to the space variable $x$.
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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.
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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.