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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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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.
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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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Journal ArticleDOI
Reviewing alternative characterizations of Meixner process
Emanuele Mazzola,Pietro Muliere +1 more
TL;DR: A review of the main characteristics and characterizations of such particular Levy processes is extracted, emphasizing the motivations for their introduction in literature as reliable financial models, together with an insight on orthogonal polynomials and an alternative path for defining the same processes as mentioned in this paper.
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Finite-pool queueing with heavy-tailed services
TL;DR: The asymptotic regime in which the population size grows to ∞ and the scaled queue-length process converges to an α-stable process with a negative quadratic drift is established to characterize the head start that is needed to create a long period of uninterrupted activity (a busy period).
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Describability via ubiquity and eutaxy in Diophantine approximation
TL;DR: In this article, the authors present a comprehensive framework for the study of the size and large intersection properties of sets of limsup type that arise naturally in Diophantine approximation and multifractal analysis.
Journal ArticleDOI
Method of Moment Estimation in Time-Changed Lévy Models
Jan Kallsen,Johannes Muhle-Karbe +1 more
TL;DR: In this article, the authors introduced a method of moment estimator for the time-changed Levy processes proposed by Carr, Geman, Madan and Yor (2003) by establishing that the returns sequence is strongly mixing with exponentially decreasing rate, and proved consistency and asymptotic normality of the resulting estimators.
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Strong existence and uniqueness for stable stochastic differential equations with distributional drift
TL;DR: In this paper, the authors considered the stochastic differential equation where the drift is a generalized function and the process is a symmetric one dimensional process, and defined the notion of solution to this equation and established strong existence and uniqueness whenever $b$ belongs to the Besov-H\"{o}lder space.