STEIN'S METHOD, GAUSSIAN PROCESSES AND PALM MEASURES, WITH APPLICATIONS TO QUEUEING

• 成果类型: Article
• 署名作者: Barbour, A. D.; Ross, Nathan; Zheng, Guangqu
• 署名单位: University of Zurich; University of Melbourne; University of Liverpool
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1908
• 发表日期: 2023
• 页码: 3835-3871
• 关键词: limit-theorem; approximations

摘要

We develop a general approach to Stein's method for approximating a random process in the path space D([0, T] -> Rd) by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as integrals with respect to an underlying point process, de-riving a general quantitative Gaussian approximation. The error bound is ex-pressed in terms of couplings of the original process to processes generated from the reduced Palm measures associated with the point process. As appli-cations, we study certain GI/GI/oo queues in the heavy traffic regime.