Rate of convergence of the conditioned random walk towards the Brownian bridge
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918292084490240 |
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| author | Decreusefond, Laurent Jacquet, Antonin |
| author_facet | Decreusefond, Laurent Jacquet, Antonin |
| contents | We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in the Glivencko-Cantelli theorem. Combining a functional Stein method with a Radon-Nikodym representation of the bridge, we bound the Fortet-Mourier distance between these conditioned processes and the Brownian bridge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rate of convergence of the conditioned random walk towards the Brownian bridge Decreusefond, Laurent Jacquet, Antonin Probability We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in the Glivencko-Cantelli theorem. Combining a functional Stein method with a Radon-Nikodym representation of the bridge, we bound the Fortet-Mourier distance between these conditioned processes and the Brownian bridge. |
| title | Rate of convergence of the conditioned random walk towards the Brownian bridge |
| topic | Probability |
| url | https://arxiv.org/abs/2601.11162 |