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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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Transform-Based Evaluation of Prices and Greeks of Lookback Options Driven by Lévy Processes
Naser M. Asghari,Michel Mandjes +1 more
TL;DR: In this paper, the authors developed a technique based on numerical inversion to compute the prices and Greeks of lookback options driven by Levy processes, where the Wiener-Hopf decomposition provides all the probabilistic information needed to evaluate these prices.
A distributional limit theorem for the realized power variation of linear fractional stable motions
TL;DR: In this article, the authors deduce a distributional theorem for the realized power variation of linear fractional stable motions by choosing the technique of subordination to reduce the proof to a Gaussian limit theorem based on Malliavin-calculus.
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Higher order Cauchy problems in bounded domains
TL;DR: In this article, Meerschaert, Nane and Vellaisamy study solutions of a class of higher-order partial differential equations in bounded domains, where the authors express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < β < 1, or by the absolute value of a symmetric α-stable process with 0 < α ≤ 2.
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Ergodicities and exponential ergodicities of Dawson-Watanabe type processes
TL;DR: In this paper, the ergodicities of the Dawson-Watanabe superprocesses without or with immigration were derived under natural assumptions and the strong Feller property in the total variation distance was derived as a byproduct.
Journal Article
Characterizations of Multivariate Normal-Poisson Model
TL;DR: In this article, a multivariate normal-Poisson model was introduced as a special case of normal stable Tweedie models, which is composed of a univariate Poisson variable, and the remaining variables given the Poisson one are independent Gaussian variable with variance the value of the poisson component.