Convergence of Reflected Langevin Diffusion for Constrained Sampling
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912836333076480 |
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| author | Mane, Tarika Boukardagha, Amine |
| author_facet | Mane, Tarika Boukardagha, Amine |
| contents | We examine the Langevin diffusion confined to a closed, convex domain $D\subset\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that their invariant measures converge, in Wasserstein-2 distance and with explicit polynomial rate, to the invariant measure of the reflected Langevin diffusion. We also analyze a time-discretization of the penalized process obtained via the Euler-Maruyama scheme and demonstrate the convergence to the original constrained measure. These results provide a rigorous approximation framework for reflected Langevin dynamics in both continuous and discrete time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00386 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of Reflected Langevin Diffusion for Constrained Sampling Mane, Tarika Boukardagha, Amine Probability Statistics Theory We examine the Langevin diffusion confined to a closed, convex domain $D\subset\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that their invariant measures converge, in Wasserstein-2 distance and with explicit polynomial rate, to the invariant measure of the reflected Langevin diffusion. We also analyze a time-discretization of the penalized process obtained via the Euler-Maruyama scheme and demonstrate the convergence to the original constrained measure. These results provide a rigorous approximation framework for reflected Langevin dynamics in both continuous and discrete time. |
| title | Convergence of Reflected Langevin Diffusion for Constrained Sampling |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2512.00386 |