Scaling limit of boundary random walks: A martingale problem approach
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915530122723328 |
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| author | Arroyave, Juan Carlos Barros, Eldon Pimenta, Eduardo |
| author_facet | Arroyave, Juan Carlos Barros, Eldon Pimenta, Eduardo |
| contents | We establish the scaling limit of a class of boundary random walks to the full spectrum of Brownian-type processes on the half-line. By solving the associated martingale problem and employing weak convergence techniques, we prove that under appropriate scaling, the process converges to the general Brownian motion in the $J_1$-Skorokhod topology. The main novelty of our approach lies in a result on the asymptotic behavior of the local time of the boundary random walks, allowing us to derive a CLT result for several Brownian-type limit processes on the half-line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling limit of boundary random walks: A martingale problem approach Arroyave, Juan Carlos Barros, Eldon Pimenta, Eduardo Probability 60F05, 60J60, 60G50, 60J65, 60J55 We establish the scaling limit of a class of boundary random walks to the full spectrum of Brownian-type processes on the half-line. By solving the associated martingale problem and employing weak convergence techniques, we prove that under appropriate scaling, the process converges to the general Brownian motion in the $J_1$-Skorokhod topology. The main novelty of our approach lies in a result on the asymptotic behavior of the local time of the boundary random walks, allowing us to derive a CLT result for several Brownian-type limit processes on the half-line. |
| title | Scaling limit of boundary random walks: A martingale problem approach |
| topic | Probability 60F05, 60J60, 60G50, 60J65, 60J55 |
| url | https://arxiv.org/abs/2507.10528 |