A note on the $\mathcal{W}_2$-convergence rate of the empirical measure of an ergodic $\mathbb{R}^d$-valued diffusion
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917918910971904 |
|---|---|
| author | Chassagneux, Jean-Francois Pagès, Gilles |
| author_facet | Chassagneux, Jean-Francois Pagès, Gilles |
| contents | In this note, we consider a Stochastic Differential Equation under a strong confluence and Lipschitz continuity assumption of the coefficients. For the unique stationary solution, we study the rate of convergence of its empirical measure toward the invariant probability measure. We provide rate for the Wasserstein distance in the mean quadratic and almost sure sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the $\mathcal{W}_2$-convergence rate of the empirical measure of an ergodic $\mathbb{R}^d$-valued diffusion Chassagneux, Jean-Francois Pagès, Gilles Probability In this note, we consider a Stochastic Differential Equation under a strong confluence and Lipschitz continuity assumption of the coefficients. For the unique stationary solution, we study the rate of convergence of its empirical measure toward the invariant probability measure. We provide rate for the Wasserstein distance in the mean quadratic and almost sure sense. |
| title | A note on the $\mathcal{W}_2$-convergence rate of the empirical measure of an ergodic $\mathbb{R}^d$-valued diffusion |
| topic | Probability |
| url | https://arxiv.org/abs/2502.07704 |