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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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Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility
TL;DR: In this paper, a second order approximation for ATM option prices is derived for a large class of exponential L evy models, with or without a Brownian component, and the formulas extend both to the case of \close-to-the-money" strikes and for the case where the continuous Brownian components is replaced by an independent stochastic volatility process with leverage.
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
Rescaling limits of the spatial Lambda-Fleming-Viot process with selection.
TL;DR: In this paper, a measure-valued dual process encoding the locations of the potential ancestors of a sample taken from such a population was proposed. But the model was not considered in this paper.
References
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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.
Book ChapterDOI
The Theory of Scale Functions for Spectrally Negative Lévy Processes
TL;DR: In this article, the authors give an up-to-date account of the theory and applications of scale functions for spectrally negative Levy processes, including the first extensive overview of how to work numerically with scale functions.
Journal ArticleDOI
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.
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.