Lévy Processes with Two-Sided Reflection

DOI10.1007/978-3-319-23138-9_2zbMath1338.60126OpenAlexW2291480101MaRDI QIDQ2807248

Mats Pihlsgård, Soren Asmussen, Lars Nørvang Andersen, Peter W. Glynn

Publication date: 19 May 2016

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-23138-9_2

zbMATH Keywords

Lévy processesPoisson's equationphase-type distributionSkorokhod problemcentral limit theoremlarge deviationsmartingaleheavy tailsintegro-differential equationlocal timefunctional limit theoremqueueing theorystorage processItō's formulafirst passage problemSiegmund dualityoverflowloss ratefinite buffer problem

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Martingales with continuous parameter (60G44) Large deviations (60F10) Stochastic functional-differential equations (34K50) Functional limit theorems; invariance principles (60F17) Local time and additive functionals (60J55) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (13)

Sticky Brownian motions and a probabilistic solution to a two-point boundary value problem ⋮ A review of Burke's theorem for Brownian motion ⋮ Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement ⋮ Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension ⋮ Lévy-driven GPS queues with heavy-tailed input ⋮ SDEs with two reflecting barriers driven by semimartingales and processes with bounded \(p\)-variation ⋮ Tightness and weak convergence of probabilities on the Skorokhod space on the dual of a nuclear space and applications ⋮ Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems ⋮ A broad view of queueing theory through one issue ⋮ Discretization error for a two-sided reflected Lévy process ⋮ Heavy-tailed random walks, buffered queues and hidden large deviations ⋮ The correlation function of a queue with Lévy and Markov additive input ⋮ Large Deviations for Additive Functionals of Reflected Jump-Diffusions

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