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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.
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.
Journal ArticleDOI
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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Modeling stochastic anomalies in an SIS system
Andrew Vlasic,Troy Day +1 more
TL;DR: In this article, a stochastic SIS model with Gaussian and Poissonian perturbations was proposed to account for noise and anomalies in the transmission rate, and conditions were given for stability to the disease free equilibrium and for positive Harris recurrence with a unique invariant measure for the endemic.
Journal ArticleDOI
The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index $\bf 1<\alpha \leq 2$
TL;DR: In this paper, the authors studied fundamental properties of the fractional, one-dimensional Weyl operator densely defined on the Hilbert space and determined the asymptotic behaviour of both the free Green's function and its variation with respect to energy for bound states.
Posted Content
Non-classical Tauberian and Abelian type criteria for the moment problem
Pierre Patie,Aditya Vaidyanathan +1 more
TL;DR: In this paper, a Tauberian type criterion for moment indeterminacy was proposed, expressed purely in terms of the asymptotic behavior of the moment sequence (and its extension to imaginary lines).
Journal ArticleDOI
Inference based on adaptive grid selection of probability transforms
Shibin Zhang,Xuming He +1 more
TL;DR: By employing a closeness measure to evaluate the asymptotic variance of the transform-based estimator, this paper proposes a statistical inference procedure, accompanied with adaptive grid selection, for parametric inference based on adaptive selection of grids.
Advanced stock price models, concave distortion functions and liquidity risk in finance
TL;DR: In this paper, the authors compare the precios of different models for opciones de barrera with the corresponding prices of the Bolsa alemana, a stock market index of the Eurozone.