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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
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Ten equivalent definitions of the fractional laplace operator
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Optimal stopping and perpetual options for Lévy processes
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Density and tails of unimodal convolution semigroups
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Extreme Events: Dynamics, Statistics and Prediction
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References
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The Dirichlet problem for nonlocal Lévy-type operators
TL;DR: In this article, the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Levy processes whose Levy measures need not be absolutely continuous is studied.
Posted Content
Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models
TL;DR: The main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component, and discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.
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Continuous-state branching processes with competition: duality and reflection at infinity
TL;DR: In this article, the boundary behavior of continuous-state branching processes with quadratic competition is studied in whole generality, and necessary and sufficient conditions are given for a stationary distribution to exist.
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Multidimensional polynomial Euler products and infinitely divisible distributions on R^d
Takahiro Aoyama,Takashi Nakamura +1 more
TL;DR: In this article, a necessary and sufficient condition for some polynomial Euler products to generate characteristic functions is given by applying the Kronecker's approximation theorem and using the Baker's theorem.
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A new family of tempered distributions
TL;DR: Tempered distributions have received considerable attention, both from a theoretical point of view and in several important application fields as mentioned in this paper, and the most popular choice is perhaps the Tweedie model, which is obtained by tempering the Positive Stable distribution.