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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.
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.
Journal ArticleDOI
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 Article
Stochastic integrals with respect to l´ evy processes and infinitely divisible distributions
TL;DR: In this paper, Lindner and Sato survey results on two topics on stochastic integrals with respect to Levy processes and infinitely divisible distributions and apply them to the problem of transforming non-random functions to infinite divisible functions.
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A multiple-curve HJM model of interbank risk
TL;DR: In this paper, the authors study the valuation of interest rate derivatives in a multiple-curve setup, which accounts for the spreads between a risk-free discount curve and LIBOR curves.
Journal ArticleDOI
Futures pricing in electricity markets based on stable CARMA spot models
TL;DR: In this paper, a non-stationary independent increments process for the low-frequency dynamics, and model the large uctuations by a nonGaussian stable CARMA process is presented.
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A statistical model of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence
TL;DR: In this paper, a simple statistical model of three-dimensionalally anisotropic, intermittent, strong Alfv\'enic turbulence, incorporating both critical balance and dynamic alignment, was proposed based on log-Poisson statistics for Elsasser-field increments along the magnetic field.
Journal ArticleDOI
Monte Carlo simulation of railway track geometry deterioration and restoration
L M Quiroga,E Schnieder +1 more
TL;DR: A new system identification method to obtain reliable simulation of the railway geometry ageing process and the presented model is extended in order to analyse the effect of the variation of factors influencing the ageing process.