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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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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.
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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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Estimates of heat kernels of non-symmetric L\'evy processes
TL;DR: In this article, the densities of non-symmetric Levy processes were investigated and upper and lower estimates of the density and its derivatives were derived for the case when the corresponding jump measure is allowed to be highly non-Symmetric and the characteristic exponent satisfies a scaling condition.
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Realized laplace transforms for pure-jump semimartingales
Viktor Todorov,George Tauchen +1 more
TL;DR: In this paper, the authors consider the stochastic scale of discretely-observed pure-jump martingales with locally stable Levy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases.
Posted Content
Levy Based Cross-Commodity Models and Derivative Valuation
TL;DR: A new cross-commodity modeling framework which accounts for jumps and cointegration in prices and introduces a new derivative valuation methodology by working in Fourier space, tailored for mean-reverting models.
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Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes
Eckhard Schlemm,Robert Stelzer +1 more
TL;DR: In this article, the class of multivariate Levy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the classes of continuous time state space models, and the linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to be exponentially completely regular.
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Asymptotic and Exact Pricing of Options on Variance
TL;DR: The small-time limits of options on both objects are characterized and it is found that the difference between them strongly depends on whether or not the stock price process has jumps.