Convergence rates for the $p$-Wasserstein distance of the empirical measures of an ergodic Markov process
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912793055199232 |
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| author | Schilling, René L. Wang, Jian Wu, Bingyao Zhu, Jie-Xiang |
| author_facet | Schilling, René L. Wang, Jian Wu, Bingyao Zhu, Jie-Xiang |
| contents | Let $X:=(X_t)_{t\geq 0}$ be an ergodic Markov process on $\real^d$, and $p>0$. We derive upper bounds of the $p$-Wasserstein distance between the invariant measure and the empirical measures of the Markov process $X$. For this we assume, e.g.\ that the transition semigroup of $X$ is exponentially contractive in terms of the $1$-Wasserstein distance, or that the iterated Poincaré inequality holds together with certain moment conditions on the invariant measure. Typical examples include diffusions and underdamped Langevin dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_22935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence rates for the $p$-Wasserstein distance of the empirical measures of an ergodic Markov process Schilling, René L. Wang, Jian Wu, Bingyao Zhu, Jie-Xiang Probability 60F15, 60F25, 60G57, 60J60 Let $X:=(X_t)_{t\geq 0}$ be an ergodic Markov process on $\real^d$, and $p>0$. We derive upper bounds of the $p$-Wasserstein distance between the invariant measure and the empirical measures of the Markov process $X$. For this we assume, e.g.\ that the transition semigroup of $X$ is exponentially contractive in terms of the $1$-Wasserstein distance, or that the iterated Poincaré inequality holds together with certain moment conditions on the invariant measure. Typical examples include diffusions and underdamped Langevin dynamics. |
| title | Convergence rates for the $p$-Wasserstein distance of the empirical measures of an ergodic Markov process |
| topic | Probability 60F15, 60F25, 60G57, 60J60 |
| url | https://arxiv.org/abs/2512.22935 |