Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913000296808448 |
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| author | Monmarché, Pierre |
| author_facet | Monmarché, Pierre |
| contents | The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors), is a well-studied question in the case where the distances are in fact deterministically contracted by the drift (global dissipativity condition) or in the case $p=1$ (with reflection couplings). This work focuses on the non-globally dissipative case with $p>1$. This situation was previously considered in \cite{MonmarcheBruit}, but only for elliptic processes, and with a restriction on the diffusivity coefficient (which had to be large enough). Here, we extend this analysis to non-elliptic processes and provide sharper conditions to get contractions along synchronous coupling, including negative results, lower bounds and a characterization (at least in dimension 1) in terms of the maximal eigenvalue of a Feynman-Kac operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity Monmarché, Pierre Probability The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors), is a well-studied question in the case where the distances are in fact deterministically contracted by the drift (global dissipativity condition) or in the case $p=1$ (with reflection couplings). This work focuses on the non-globally dissipative case with $p>1$. This situation was previously considered in \cite{MonmarcheBruit}, but only for elliptic processes, and with a restriction on the diffusivity coefficient (which had to be large enough). Here, we extend this analysis to non-elliptic processes and provide sharper conditions to get contractions along synchronous coupling, including negative results, lower bounds and a characterization (at least in dimension 1) in terms of the maximal eigenvalue of a Feynman-Kac operator. |
| title | Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity |
| topic | Probability |
| url | https://arxiv.org/abs/2603.00773 |