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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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Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions
TL;DR: In this paper, the limits of the nested sequences of the ranges of the iterations of the iteration of a Levy process on infinitely divisible distributions were studied. And the class of completely self-decomposable distributions with weak mean 0 was defined.
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Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields
TL;DR: In this paper, a measure of dependence called ''theta$-lex weak dependence'' was proposed for stationary random fields, which is more general than strong mixing, i.e., it applies to a broader class of models.
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On Deterministic Markov Processes: Expandability and Related Topics
TL;DR: In this article, the class of universal Markov processes on R d which do not depend on random is studied and the semimartingale property is characterized in terms of the jumps of a one-dimensional deterministic Markov process.
Journal ArticleDOI
Inference on the Lévy measure in case of noisy observations
TL;DR: In this article, an extension of the pre-averaging method allows for a consistent estimation of the associated spectral function, and the asymptotic behaviour of the novel estimator is the same as without noise.
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Nonparametric estimation of mark’s distribution of an exponential shot-noise process
TL;DR: In this article, a nonlinear inverse problem occurring in nuclear science is considered, where gamma rays randomly hit a semiconductor detector which produces an impulse response of electric current, known as pileup.
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.