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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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Fluctuations of Lévy Processes with Applications
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Ten equivalent definitions of the fractional laplace operator
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Optimal stopping and perpetual options for Lévy processes
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Density and tails of unimodal convolution semigroups
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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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Heat Kernel Upper Estimates for Symmetric Jump Processes with Small Jumps of High Intensity
TL;DR: In this paper, the authors considered the transition density of the associated symmetric Markov jump process X and proved upper estimates for the associated transition density in terms of the transition probability β ∈ (0, 1).
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Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows
TL;DR: In this article, a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Levy measures were established. But these were restricted to symmetric stable self-similar processes with stationary increments that coincide on a part of its parameter space with a previously described process.
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Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
TL;DR: The joint a priori distribution of the samples is derived and it is shown how this probability density function can be factorized, enabling us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns.
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Deep factorisation of the stable process
TL;DR: In this article, a matrix Wiener-Hopf factorisation of the matrix exponent of the Lamperti-stable Markov Process (LMP) has been proposed for two-sided hopping Markov processes.
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A unifying approach to fractional Lévy processes
TL;DR: In this paper, a unifying approach for fractional L evy processes is presented, where kernels of the form a((t s) + ( s)+ + + b(( t s) (s) ), where can be chosen according to the existing moments and the Blumenthal-Getoor index of the underlying Levy process.