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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.19710 |
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| _version_ | 1866908406172876800 |
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| author | Guang, Jin Chen, Xinyun Dai, J. G. Glynn, Peter W. |
| author_facet | Guang, Jin Chen, Xinyun Dai, J. G. Glynn, Peter W. |
| contents | Inspired by Dai et al. [2023], we develop a novel multi-scaling asymptotic regime for semimartingale reflecting Brownian motion (SRBM). In this regime, we establish the steady-state convergence of SRBM to a product-form limit with exponentially distributed components by assuming the P-reflection matrix and a uniform moment bound condition. We further demonstrate that the uniform moment bound condition holds in several subclasses of P-matrices. Our proof approach is rooted in the basic adjoint relationship (BAR) for SRBM proposed by Harrison and Williams [1987a]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime Guang, Jin Chen, Xinyun Dai, J. G. Glynn, Peter W. Probability Inspired by Dai et al. [2023], we develop a novel multi-scaling asymptotic regime for semimartingale reflecting Brownian motion (SRBM). In this regime, we establish the steady-state convergence of SRBM to a product-form limit with exponentially distributed components by assuming the P-reflection matrix and a uniform moment bound condition. We further demonstrate that the uniform moment bound condition holds in several subclasses of P-matrices. Our proof approach is rooted in the basic adjoint relationship (BAR) for SRBM proposed by Harrison and Williams [1987a]. |
| title | Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime |
| topic | Probability |
| url | https://arxiv.org/abs/2503.19710 |