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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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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.
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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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Sufficientness postulates for Gibbs-type priors and hierarchical generalizations
TL;DR: In particular, this article revisited and discussed the sufficientness postulate for the two parameter Poisson-Dirichlet prior within the more general framework of Gibbs-type priors and their hierarchical generalizations.
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Path Decomposition of Ruinous Behaviour for a General Lévy Insurance Risk Process
Philip S. Griffin,Ross A. Maller +1 more
TL;DR: In this article, the authors analyse the general Levy insurance risk process for Levy measures in the convolution equivalence class S(α), α > 0, via a new kind of path decomposition.
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Multivariate FX models with jumps: Triangles, Quantos and implied correlation
TL;DR: An integrated model of the joint dynamics of FX rates and asset prices for the pricing of FX derivatives, including Quanto products is proposed, based on a multivariate construction for Levy processes which proves to be analytically tractable.
Journal ArticleDOI
Stochastic Analysis of Reaction–Diffusion Processes
TL;DR: The master equation for spatially discretized systems involving reaction and diffusion is developed and an estimator for the appropriate compartment size for simulating reaction–diffusion systems is discussed and a measure of fluctuations in a discretization system is introduced.
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A Parametrix Approach for some Degenerate Stable Driven SDEs
Lorick Huang,Stéphane Menozzi +1 more
TL;DR: In this article, the authors considered a stable driven degenerate stochastic differential equation whose coefficients satisfy a kind of weak H{''o}rmander condition and proved the uniqueness of the martingale problem for the associated generator under some dimension constraints.