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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
Citations
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Book ChapterDOI
On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws
Reiichiro Kawai,Junichi Imai +1 more
TL;DR: In this article, the authors discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series and investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation.
Book ChapterDOI
Transport in a Stochastic Goupillaud Medium
TL;DR: In this article, Fourier integral operators are used to model wave propagation in one-dimensional transport, and a partial aspect is addressed, namely explicit models of stochastic, highly irregular transport speeds in one dimensional transport, which will form the basis for more complex models.
Journal ArticleDOI
Existence of a density of the 2-dimensional Stochastic Navier Stokes Equation driven by Lévy processes or fractional Brownian motion
TL;DR: In this paper, the authors investigated the regularity properties of the probability measure induced by the solution process induced by a Levy process or a fractional Brownian motion driven Navier-Stokes equations on the two-dimensional torus T.
Dissertation
Small-time asymptotics of call prices and implied volatilities for exponential Lévy models
Journal ArticleDOI
Generalized Barndorff-Nielsen and Shephard Model and Discretely Monitored Option Pricing
TL;DR: In this paper, a generalized Barndorff-Nielsen and Shephard model is proposed, in which the log return on an asset price is governed by a Levy process with stochastic volatility modeled by a non-Gaussian Ornstein-Uhlenbeck process.
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.