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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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Journal ArticleDOI
Behaviors of multivariable finite Euler products in probabilistic view
Takahiro Aoyama,Takashi Nakamura +1 more
TL;DR: In this paper, the authors studied multivariable finite Euler products and showed how they behave in view of such properties, including functions which generate infinitely divisible, not necessarily divisible characteristic functions and not even to be characteristic functions.
Journal ArticleDOI
On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions
TL;DR: In this paper, the authors developed new parametric families of min-stable multivariate exponential (MSMVE) distributions in arbitrary dimensions and provided a convenient stochastic representation for such models, which is helpful with regard to sampling strategies.
Posted Content
On the stochastic behaviour of optional processes up to random times
TL;DR: In this article, a study of random times on filtered probability spaces is undertaken and it is shown that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random times is actually a randomised stopping time.
Proceedings ArticleDOI
Real-Time Inference for a Gamma Process Model of Neural Spiking
TL;DR: This work extends previous Bayesian nonparametric models of neural spiking to jointly detect and cluster neurons using a Gamma process model, and develops an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-the-art.
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.