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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
Citations
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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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Stochastic integral representations and classification of sum- and max-infinitely divisible processes
Zakhar Kabluchko,Stilian Stoev +1 more
TL;DR: In this paper, it was shown that a stationary, stochastically continuous, sum- or max-i.i.d. random process can be generated by a measure-preserving flow on a finite Borel measure space and that this flow is unique.
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Approximation of skewed and leptokurtic return distributions
TL;DR: In this article, the authors present the practical implementation of these two distributions by presenting how the density functions can be computed efficiently by applying the Fast Fourier Transform (FFT) and how standardization helps to drive efficiency and effectiveness of maximum likelihood inference.
Posted Content
Lecture Notes on Stochastic Processes
Alexander Gasnikov,Eduard Gorbunov,S. A. Guz,Elena Chernousova,Maksim Shirobokov,Egor Shulgin +5 more
TL;DR: In the course "Stochastic Processes" as discussed by the authors, the authors presented a course on correlation theory, Markov processes, and the secretary problem for third-year students at the Russian Institute of Physics and Technology.
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Diffusions on a space of interval partitions: Poisson–Dirichlet stationary distributions
TL;DR: In this paper, the authors introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters α,0 and α,α.
Non-life Insurance Mathematics
TL;DR: In this paper, the authors describe the basic facts of non-life insurance and then explain risk processes, in particular the asymptotic behavior of the probability that an insurance product may end up in ruin during its lifetime.