Short-time existence and uniqueness for some infinite-dimensional Nash systems
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908731431714816 |
|---|---|
| author | Redaelli, Davide Francesco |
| author_facet | Redaelli, Davide Francesco |
| contents | We prove local (in time) existence and uniqueness for a class of infinite-dimensional Nash systems, namely systems of infinitely many Hamilton-Jacobi-Bellman equations set in an infinite-dimensional Euclidean space. Such systems have been recently showed (see arXiv:2401.06534) to arise in the theory of stochastic differential games with interactions governed by sparse graphs, under structural assumptions that inspired the hypotheses exploited in the present work. Contextually, we also prove a general linear result, providing a priori estimates, stable with respect to the dimension, for transport-diffusion equations whose drifts (and their derivatives) enjoy appropriate decay properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Short-time existence and uniqueness for some infinite-dimensional Nash systems Redaelli, Davide Francesco Analysis of PDEs 35A01, 35A02, 35R15, 35G50, 91A07 We prove local (in time) existence and uniqueness for a class of infinite-dimensional Nash systems, namely systems of infinitely many Hamilton-Jacobi-Bellman equations set in an infinite-dimensional Euclidean space. Such systems have been recently showed (see arXiv:2401.06534) to arise in the theory of stochastic differential games with interactions governed by sparse graphs, under structural assumptions that inspired the hypotheses exploited in the present work. Contextually, we also prove a general linear result, providing a priori estimates, stable with respect to the dimension, for transport-diffusion equations whose drifts (and their derivatives) enjoy appropriate decay properties. |
| title | Short-time existence and uniqueness for some infinite-dimensional Nash systems |
| topic | Analysis of PDEs 35A01, 35A02, 35R15, 35G50, 91A07 |
| url | https://arxiv.org/abs/2411.18356 |