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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.04935 |
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| _version_ | 1866929533143220224 |
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| author | Chaintron, Louis-Pierre |
| author_facet | Chaintron, Louis-Pierre |
| contents | A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework allows for degenerate diffusion matrices, which may depend on the empirical measure, including mean-field kinetic processes. The main tool is an extension of Tanaka's pathwise construction to non-constant diffusion matrices. This can be seen as a mean-field analogous of Azencott's quasi-continuity method for the Freidlin-Wentzell theory. As a by-product, uniform-in-time-step fluctuation and large deviation estimates are proved for a discrete-time version of the meanfield system. Uniform-in-time-step convergence is also proved for the value function of some mean-field control problems with quadratic cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-continuity method for mean-field diffusions: large deviations and central limit theorem Chaintron, Louis-Pierre Probability A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework allows for degenerate diffusion matrices, which may depend on the empirical measure, including mean-field kinetic processes. The main tool is an extension of Tanaka's pathwise construction to non-constant diffusion matrices. This can be seen as a mean-field analogous of Azencott's quasi-continuity method for the Freidlin-Wentzell theory. As a by-product, uniform-in-time-step fluctuation and large deviation estimates are proved for a discrete-time version of the meanfield system. Uniform-in-time-step convergence is also proved for the value function of some mean-field control problems with quadratic cost. |
| title | Quasi-continuity method for mean-field diffusions: large deviations and central limit theorem |
| topic | Probability |
| url | https://arxiv.org/abs/2410.04935 |