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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
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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.
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.
Journal ArticleDOI
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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Heat kernel estimates for symmetric jump processes with mixed polynomial growths
TL;DR: In this paper, the transition densities of pure-jump symmetric Markov processes with mixed polynomial growth were studied. And they were shown to be equivalent to the Khintchine-type law of iterated logarithm at the infinity.
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Monotone increment processes, classical Markov processes, and Loewner chains
TL;DR: In this article, it was shown that decreasing Loewner chains in the upper half-plane correspond to quantum stochastic processes of unitary operators with monotonically independent multiplicative increments.
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Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations
TL;DR: In this paper, the authors consider a jump-type Cox-Ingersoll-Ross (CIR) process driven by a standard Wiener process and a subordinator, and study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate.
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On the roughness of the paths of RBM in a wedge
TL;DR: In this paper, it was shown that on excursion intervals of Z away from the origin, (Z,Y ) satisfies the standard Skorokhod problem for X, but not on the entire time horizon.
Journal ArticleDOI
Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes∗
Yuji Umezawa,Akira Yamazaki +1 more
TL;DR: In this paper, a backward recurrence relation for computing multivariate characteristic functions of the intertemporal joint distribution of time-changed Levy processes is derived for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a timechanged Levy process.