Abstract
We develop a general approach to Stein’s method for approximating a random process in the path space 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 queues in the “heavy traffic” regime.
Citation
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. https://doi.org/10.1214/22-AAP1908
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