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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
Citations
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An overshoot approach to recurrence and transience of Markov processes
TL;DR: In this article, the authors develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between + ∞ and − ∞, based on a Markov chain which only consists of jumps (overshoots) of the process into complementary parts of the state space.
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Limit theorems for the empirical distribution function of scaled increments of It\^{o} semimartingales at high frequencies
Viktor Todorov,George Tauchen +1 more
TL;DR: In this article, the authors derived limit theorems for the empirical distribution function of devolatilized increments of an Ito semimartingale observed at high frequencies, which are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and large jumps.
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Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity
Sylvie Méléard,Sepideh Mirrahimi +1 more
TL;DR: In this paper, an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or non-local reaction terms is presented, based on the exponential speed of propagation of the population.
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Limit theory for high frequency sampled MCARMA models
TL;DR: In this paper, a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid is considered and the asymptotic behavior of the properly normalized partial sum to a stable or a normal random vector is derived.
Journal ArticleDOI
Cortical spatiotemporal dimensionality reduction for visual grouping
TL;DR: A spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher-dimensional spaces is defined and how these connectivities can be used to obtain low-level object segmentation is shown.
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.