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October 2023 Stein’s method, Gaussian processes and Palm measures, with applications to queueing
A. D. Barbour, Nathan Ross, Guangqu Zheng
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Ann. Appl. Probab. 33(5): 3835-3871 (October 2023). DOI: 10.1214/22-AAP1908


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, deriving a general quantitative Gaussian approximation. The error bound is expressed in terms of couplings of the original process to processes generated from the reduced Palm measures associated with the point process. As applications, we study certain GI/GI/ queues in the “heavy traffic” regime.


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A. D. Barbour. Nathan Ross. Guangqu Zheng. "Stein’s method, Gaussian processes and Palm measures, with applications to queueing." Ann. Appl. Probab. 33 (5) 3835 - 3871, October 2023.


Received: 1 October 2021; Revised: 1 September 2022; Published: October 2023
First available in Project Euclid: 3 November 2023

Digital Object Identifier: 10.1214/22-AAP1908

Primary: 60G15 , 60G55
Secondary: 60F25 , 60K25

Keywords: Gaussian processes , GI/GI/∞ queue , Palm measure , Stein’s method

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.33 • No. 5 • October 2023
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