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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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Posted Content
Trace estimates for unimodal L\'evy processes
TL;DR: In this paper, a two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal Levy processes satisfying the weak scaling conditions is given.
Journal ArticleDOI
Long-time heat kernel estimates and upper rate functions of Brownian motion type for symmetric jump processes
Yuichi Shiozawa,Jian Wang +1 more
TL;DR: In this paper, the authors obtained two-sided heat kernel estimates of large time for symmetric jump processes whose jumping kernels are comparable to the heat kernel of the Brownian process.
Journal ArticleDOI
Hunt’s Hypothesis (H) for the Sum of Two Independent Lévy Processes
Ze-Chun Hu,Wei Sun +1 more
TL;DR: In this article, the authors consider the problem of determining whether one-dimensional Levy processes satisfy Hunt's hypothesis (H) from the point of view of the sum of two independent Levy processes.
Dissertation
A stochastic equation with censored jumps related to multi-scale Piecewise Deterministic Markov Processes
TL;DR: In this paper, the authors studied the properties of d-dimensional jump type diffusion with infinitesimal generator given by Lψ(x) = 1/2 ∑ aᵤᵥ(x)/∂xᵥ∂∂ xᵥ + g(x),∇ψ (x) + ∫ (ψ,x + c(z, x)) − ψ, x)µ(dz) where µ is of infinite total mass, and gave sufficient conditions in order to obtain existence and uniqueness of
Posted Content
Limits of random walks with distributionally robust transition probabilities
TL;DR: In this paper, the authors consider a nonlinear random walk which is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition probability of a fixed Levy process.
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.