The weak convergence of regenerative processes using some excursion path decompositions

DOI10.1214/12-AIHP531zbMath1291.60179arXiv1202.2878OpenAlexW2950324611MaRDI QIDQ2451108

Florian Simatos, Amaury Lambert

Publication date: 26 May 2014

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2878

zbMATH Keywords

weak convergenceregenerative processexcursion theoryqueueing theoryexcursion measure

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) General theory of stochastic processes (60G07) Local time and additive functionals (60J55) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20) Renewal theory (60K05)

Related Items (8)

Conjectures on symmetric queues in heavy traffic ⋮ A stochastic network with mobile users in heavy traffic ⋮ On a skew stable Lévy process ⋮ Functional limit theorems for processes pieced together from excursions ⋮ Functional limit theorems for random walks perturbed by positive alpha-stable jumps ⋮ Serve the shortest queue and Walsh Brownian motion ⋮ Limit theorems for local times and applications to SDEs with jumps ⋮ Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

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