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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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On Mittag-Leffler distributions and related stochastic processes
TL;DR: A type-2 Mittag-Leffler process turns out to be the Siegmund dual to Neveu's CSBP block-counting process arising in sampling from P D ( e - t , 0 ) .
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Fractional P(ϕ)1-processes and Gibbs measures
Kamil Kaleta,József Lőrinczi +1 more
TL;DR: In this article, the existence of fractional P ( ϕ ) 1 -processes with Kato-decomposable potentials has been proved and conditions of its uniqueness and support relating this with intrinsic ultracontractivity properties of the semigroup.
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On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling
TL;DR: This work proves the existence of a broad class of sparse processes by using the Minlos–Bochner theorem and applies the main theorem of existence to two specific subclasses of processes with specific invariance properties.
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High-order short-time expansions for ATM option prices of exponential Lévy models
TL;DR: In this paper, a second-order approximation for at-the-money (ATM) option prices is derived for a large class of exponential Levy models with or without a Brownian component, which shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration.
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Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization
Pierre Patie,Mladen Savov +1 more
TL;DR: In this paper, a representation of the Mellin transform of the exponential functional of the Levy process in terms of generalized Weierstrass products is presented, and a multiplicative Wiener-Hopf factorization generalizing previous results obtained by Patie and Savov is obtained.