Stein's method, Gaussian processes and Palm measures, with applications to queueing
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866909079739301888 |
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| author | Barbour, A. D. Ross, Nathan Zheng, Guangqu |
| author_facet | Barbour, A. D. Ross, Nathan Zheng, Guangqu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10365 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stein's method, Gaussian processes and Palm measures, with applications to queueing Barbour, A. D. Ross, Nathan Zheng, Guangqu Probability Primary 60G15, 60G55, secondary 60K25, 60F25 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. |
| title | Stein's method, Gaussian processes and Palm measures, with applications to queueing |
| topic | Probability Primary 60G15, 60G55, secondary 60K25, 60F25 |
| url | https://arxiv.org/abs/2110.10365 |