Open AccessBook
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
Citations
More filters
Proceedings ArticleDOI
Relations between information and estimation in scalar Lévy channels
TL;DR: In this paper, the authors introduce the natural family of scalar Lévy channels where the distribution of the output conditioned on the input is infinitely divisible, and establish new representations relating the mutual information between the channel input and output to an optimal estimation loss, thereby unifying and considerably extending results from the Gaussian and Poisson settings.
Journal ArticleDOI
Tail Probabilities of Subadditive Functionals of Lévy Processes
TL;DR: In this paper, the authors studied the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of Levy processes, and showed that only the points of the process that lie above a certain curve contribute to the value of the functional.
Journal ArticleDOI
Extreme statistics of anomalous subdiffusion following a fractional Fokker-Planck equation: subdiffusion is faster than normal diffusion
TL;DR: In this article, the authors investigated extreme statistics of searchers which move by anomalous subdiffusion and proved that extreme FPTs of sub-diffusion are faster than normal FPT of normal diffusion.
Journal ArticleDOI
Option pricing and hedging under a stochastic volatility Lévy process model
TL;DR: In this article, a stochastic volatility model with a Levy driving process was discussed and applied to option pricing and hedging, and the closed-form solution for the hedge ratio was obtained by applying locally risk-minimizing hedging.
Journal ArticleDOI
Asymptotic behaviour and estimates of slowly varying convolution semigroups
TL;DR: In this paper, the transition densities of isotropic unimodal convolution semigroups of probability measures were derived under the assumption that the Levy-Khintchine exponent varies slowly.
References
More filters
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.