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

Abstract

We develop a general approach to Stein's method for approximating a random process in the path space $D([0,T]\to R^d)$ 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 anunderlying 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 $\text{GI}/\text{GI}/\infty$ queues in the "heavy traffic" regime.

arXiv comment40 pages

References in corpus (9)

• Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• On many-server queues in heavy traffic
• Stein's method for multivariate Brownian approximations of sums under dependence
• Functional approximations with Stein's method of exchangeable pairs
• Donsker's theorem in {Wasserstein}-1 distance
• Stein's method of exchangeable pairs in multivariate functional approximations
• Note on A. Barbour's paper on Stein's method for diffusion approximations
• Diffusive limits of Lipschitz functionals of Poisson measures

Cited by in corpus (2)

• Stein's method, smoothing and functional approximation
• Gaussian Approximation and Moderate Deviations of Poisson Shot Noises with Application to Compound Generalized Hawkes Processes