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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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Journal ArticleDOI
A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models
Raymond Brummelhuis,Ron Chan +1 more
TL;DR: In this article, Radial Basis Function (RBF) interpolation is used to price options in exponential Levy models by numerically solving the fundamental pricing PIDE (Partial integro-differential equations).
Posted Content
A Jump type SDE approach to positive self-Similar Markov processes
Leif Döring,Matyas Barczy +1 more
TL;DR: In this paper, a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti's transformation via jump type SDEs is presented.
Posted ContentDOI
Phylofactorization - a graph partitioning algorithm to identify phylogenetic scales of ecological data
Alex D. Washburne,Justin D. Silverman,James T. Morton,Daniel J. Becker,Daniel E. Crowley,Sayan Mukherjee,Lawrence A. David,Raina K. Plowright +7 more
TL;DR: This work generalizes phylofactorization beyond relative abundances to a graph-partitioning algorithm for traits and community-ecological data from any exponential-family distribution, and introduces a phylogenetic analysis of variance which refines the understanding of the major sources of variation in the human gut.
Journal ArticleDOI
Growth-fragmentation processes and bifurcators
TL;DR: In this article, it was shown that two growth-fragmentations associated respectively with two processes with different laws may have the same distribution, if the process is a bifurcator.
Journal ArticleDOI
Distributional representations and dominance of a L\'{e}vy process over its maximal jump processes
TL;DR: In this paper, distributional identities for a Levy process, its quadratic variation process, and its maximal jump processes are derived, and used to make "small time" (as $t\downarrow0$) asymptotic comparisons between them.