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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
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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.
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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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A Unified Approach to the Heavy-Traffic Analysis of the Maximum of Random Walks
Seva Shneer,Vitali Wachtel +1 more
TL;DR: In this paper, the authors investigated the asymptotic behavior of families of random walks from the domain of attraction of a stable law and gave two elementary proofs of their main result, using each of these approaches.
Book
The Asymptotic Behavior of the Term Structure of Interest Rates
TL;DR: In this article, the authors investigate long-term interest rates in the post-crisis interest rate market, i.e., interest rates with maturity going to infinity, and analyze the properties as well as the interrelations of these properties.
Journal ArticleDOI
Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws
TL;DR: Two stochastic representations of multivariate geometric distributions are analyzed and the exchangeable narrow-sense law is furthermore shown to exhibit the multivariate right tail increasing (MRTI) dependence.
Journal ArticleDOI
A criterion for invariant measures of Itô processes based on the symbol
Anita Behme,Alexander Schnurr +1 more
TL;DR: In this paper, an integral criterion for the existence of an invariant measure of an Ito process is developed, which is based on the probabilistic symbol of the Ito Process.
Journal ArticleDOI
Sequential Testing Problems for Lévy Processes
Bruno Buonaguidi,Pietro Muliere +1 more
TL;DR: In this article, the authors presented the sequential testing of two simple hypotheses for a large class of Levy processes, and the exact solution for sequentially testing two simple hypothesis concerning the parameter p, 0, < p < 1, of a negative binomial process is explicitly given.