Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift

DOI10.1016/J.SPA.2018.03.012zbMath1403.60038arXiv1510.06955OpenAlexW2962822939MaRDI QIDQ1713469

Bart Kamphorst, Bert Zwart

Publication date: 25 January 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.06955

zbMATH Keywords

\(M/G/1\) queueheavy trafficlarge deviationsfirst passage timeuniform asymptoticscompound Poisson processsupremum

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Queueing theory (aspects of probability theory) (60K25)

Cites Work

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• On the transition from heavy traffic to heavy tails for the \(M/G/1\) queue: the regularly varying case
• Uniform large deviations for heavy-tailed queues under heavy traffic
• Large deviations for random walks under subexponentiality: The big-jump domain
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• On the longest service time in a busy period of the M/G/1 queue
• Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and first passage probabilities
• Large deviations results for subexponential tails, with applications to insurance risk
• Ruin probabilities and overshoots for general Lévy insurance risk processes
• Fluctuations of Lévy processes with applications. Introductory lectures
• Discrete and continuous time modulated random walks with heavy-tailed increments
• On the optimal dividend problem for a spectrally negative Lévy process
• Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times
• Tail asymptotics for exponential functionals of Lévy processes
• Tail Asymptotics for the Busy Period in the GI/G/1 Queue
• Stochastic-Process Limits
• Limits and Approximations for the Busy-Period Distribution in Single-Server Queues
• Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes
• The Theory of Scale Functions for Spectrally Negative Lévy Processes
• Conditioned limit theorems for random walks with negative drift
• An Extremal Problem in Probability Theory
• Asymptotic Analysis of Random Walks
• Lévy processes with adaptable exponent
• On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1
• Heavy Traffic Limit Theorems for Queues: A Survey
• Exponential spectra as a tool for the study of server-systems with several classes of customers
• Applied Probability and Queues
• An Introduction to Heavy-Tailed and Subexponential Distributions
• Upper Bounds for the Maximum of a Random Walk with Negative Drift

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