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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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DissertationDOI
Estimation techniques and goodness-of-fit tests for certain copula classes in large dimensions
Journal ArticleDOI
Multilevel particle filters for Lévy-driven stochastic differential equations
TL;DR: In this paper, a multilevel particle filter is proposed to address the computational issues involved in solving these continuum problems, and it is shown via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Levy proccess, the cost to obtain MSE scales like
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Some Theorems on Feller Processes: Transience, Local Times and Ultracontractivity
René L. Schilling,Jian Wang +1 more
TL;DR: In this article, sufficient conditions for the transience and the existence of local times of a Feller process and the ultracontractivity of the associated Feller semigroup are presented.
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Fluctuation theory for upwards skip-free L\'evy chains
TL;DR: In this article, a fluctuation theory and a theory of scale functions are developed for upwards skip-free L\'evy chains, i.e. for right-continuous random walks embedded into continuous time as compound Poisson processes.
Journal ArticleDOI
Truncated Realized Covariance when prices have infinite variation jumps
TL;DR: In this article, the authors show that the convergence of the Truncated Realized Covariance (TRC) to the Integrated Covariation between the Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation (iV), through both the degree of dependence and the jump activity indices of the two small jumps processes.