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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
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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Superposition of COGARCH processes
TL;DR: In this paper, three superpositions of COGARCH (sup-CO-GARCH) volatility processes driven by Levy processes or Levy bases are proposed, and the second-order properties, jump behaviour, and jump behavior is investigated.
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Joint asymptotic distribution of certain path functionals of the reflected process
TL;DR: In this article, the authors investigated the joint asymptotic distribution of the reflected process of a Levy process and the path functionals of the path functions of the Levy process for a certain non-linear curve.
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On distributions of exponential functionals of the processes with independent increments
TL;DR: In this article, the density of the exponential functionals of the processes of the Levy process with independent increments was studied and sufficient conditions for the existence of smooth density of these functionals were given.
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Characterizing Physically Transient Antennas
TL;DR: This paper revisits the classical antenna figures-of-merit such as resonant frequency and input impedance, and proposes a novel immersion-time-dependent description framework to characterize this class of antennas, taking into account their PT nature.
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A generalized Avikainen’s estimate and its applications
TL;DR: This article generalizes the rate of convergence for numerical schemes for solutions of one-dimensional stochastic differential equations (SDEs) driven by Brownian motion with irregular coefficients and payoffs which are related to multilevel Monte Carlo method.