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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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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.
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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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On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes
TL;DR: In this paper, the authors studied subexponential tail asymptotics for the distribution of the maximum M t ≔ sup u ∈ [ 0, t ] X u of a process X t with negative drift for the entire range of t > 0.
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An Equilibrium Model for Spot and Forward Prices of Commodities
TL;DR: In this article, the authors consider a market model that consists of financial investors and producers of a commodity and prove the existence of an equilibrium in an abstract setting, in a framework where the consumers' demand and the exogenously priced financial market are correlated.
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Basic MAC Scheme for RF Energy Harvesting Wireless Sensor Networks: Throughput Analysis and Optimization.
TL;DR: This paper considers a basic MAC scheme, rooted in ALOHA, in which a sensor node repeats harvesting energy, backing off for a while and transmitting a packet, and develops an analytical method to exactly calculate the throughput that thebasic MAC scheme can attain.
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Selfdecomposability of moving average fractional Levy processes
Serge Cohen,Makoto Maejima +1 more
TL;DR: In this article, the authors studied the relationship between the selfdecomposability of marginal distributions or finite dimensional distributions of moving average fractional Levy processes and distributions of their driving Levy processes.
On the exponential moments of additive processes with the structure of semimartingales
TL;DR: In this article, the exponential moments of R-valued additive processes with the strucure of semimartingales, which are regarded as the Laplace transforms of the laws of these additive processes, are explicitly represented by their characteristics.