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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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Journal ArticleDOI
On the fractional Poisson process and the discretized stable subordinator
TL;DR: In this paper, the renewal counting number process N = N(t) is considered as a forward march over the non-negative integers with independent identically distributed waiting times, and the Laplace transform with respect to both variables x and t is applied.
Journal ArticleDOI
Integer‐valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes
TL;DR: In this article, the authors introduce a new continuous-time framework for modelling serially correlated count and integer-valued data and apply it to high-frequency financial data, where the key component in their new model is the class of integervalued trawl processes, which are serially correlation, stationary, infinitely divisible processes.
Posted Content
Completely monotonic gamma ratio and infinitely divisible H-function of Fox
TL;DR: In this article, the authors investigated conditions for logarithmic complete monotonicity of a quotient of two products of gamma functions, where the argument of each gamma function has different scaling factor.
Journal ArticleDOI
Realized Laplace transforms for estimation of jump diffusive volatility models
TL;DR: In this paper, the authors developed an efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps, which involves first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model free estimate of the daily integrated empirical Laplace transform of the unobservable volatility.
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MMSE Estimation of Sparse Lévy Processes
TL;DR: This work investigates a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Lévy process are corrupted by noise, and proposes a novel non-iterative implementation of the MMSE estimator based on the belief-propagation (BP) algorithm performed in the Fourier domain.
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.