Tail asymptotics for the maximum of perturbed random walk

DOI10.1214/105051606000000268zbMath1118.60073arXivmath/0610271OpenAlexW3100822211MaRDI QIDQ862212

Victor F. Araman, Peter W. Glynn

Publication date: 5 February 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610271

zbMATH Keywords

functional limit theoremsrandom walksperformance evaluationqueueing theoryqueues and servicetraffic problems

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Traffic problems in operations research (90B20) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Functional limit theorems; invariance principles (60F17)

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Solutions to complex smoothing equations ⋮ Importance sampling for maxima on trees ⋮ On the Maximum Exceedance of a Sequence of Random Variables Over a Renewal Threshold ⋮ Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree ⋮ Convergence to the maximum process of a fractional Brownian motion with shot noise ⋮ Diffusion approximations for the maximum of a perturbed random walk ⋮ A renewal theorem and supremum of a perturbed random walk ⋮ Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims ⋮ Tail Asymptotics of the Supremum of a Regenerative Process ⋮ On Perturbed Random Walks ⋮ Power and exponential moments of the number of visits and related quantities for perturbed random walks

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