Stein's method, Gaussian processes and palm measures, with applications to queueing

DOI10.1214/22-aap1908arXiv2110.10365MaRDI QIDQ6187479

Guangqu Zheng, Nathan Ross, Andrew David Barbour

Publication date: 15 January 2024

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

Full work available at URL: https://arxiv.org/abs/2110.10365

zbMATH Keywords

Gaussian processesStein's methodpalm measure\(GI/GI/ \infty\) queue

Mathematics Subject Classification ID

Gaussian processes (60G15) Queueing theory (aspects of probability theory) (60K25) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) (L^p)-limit theorems (60F25)

Cites Work

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• Fundamentals of Stein's method
• Note on A. Barbour's paper on Stein's method for diffusion approximations
• On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces
• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• Stein's method for diffusion approximations
• Two moments suffice for Poisson approximations: The Chen-Stein method
• A heavy-traffic analysis of a closed queueing system with a \(GI/\infty\) service center
• Functional approximations via Stein's method of exchangeable pairs
• Approximation of Hilbert-valued gaussians on Dirichlet structures
• Stein's method of exchangeable pairs in multivariate functional approximations
• Donsker's theorem in Wasserstein-1 distance
• Stein's method for multivariate Brownian approximations of sums under dependence
• Stein's method for diffusive limits of queueing processes
• Stein's method for the Poisson-Dirichlet distribution and the Ewens sampling formula, with applications to Wright-Fisher models
• On many-server queues in heavy traffic
• Large ball probabilities, Gaussian comparison and anti-concentration
• On limit laws for service processes in multi-channel systems
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator
• Normal Approximation by Stein’s Method
• On the heavy-traffic limit theorem for GI/G/∞ queues
• Uniform rates of convergence for Markov chain transition probabilities
• Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
• Random Fields and Geometry
• Limiting diffusion approximations for the many server queue and the repairman problem
• An Introduction to the Theory of Point Processes

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