Long time behaviour of Mean Field Games with fractional diffusion
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909606087753728 |
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| author | Ersland, Olav Jakobsen, Espen Robstad Porretta, Alessio |
| author_facet | Ersland, Olav Jakobsen, Espen Robstad Porretta, Alessio |
| contents | In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift term, while being confined by an external field in order to guarantee ergodicity. In the case of globally Lipschitz, locally uniformly convex Hamiltonian, and weakly coupled costs satisfying the Lasry-Lions monotonicity condition, we prove that there is a unique solution $(u_T,m_T)$ to the mean field game problem in $(0,T)$ and we show that, if $T$ is sufficiently large, $(u_T,m_T)$ satisfies the so-called turnpike property, namely it is exponentially close to the (unique) stationary ergodic state for any proportionally long intermediate time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long time behaviour of Mean Field Games with fractional diffusion Ersland, Olav Jakobsen, Espen Robstad Porretta, Alessio Analysis of PDEs In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by independent jump processes and controlled through the drift term, while being confined by an external field in order to guarantee ergodicity. In the case of globally Lipschitz, locally uniformly convex Hamiltonian, and weakly coupled costs satisfying the Lasry-Lions monotonicity condition, we prove that there is a unique solution $(u_T,m_T)$ to the mean field game problem in $(0,T)$ and we show that, if $T$ is sufficiently large, $(u_T,m_T)$ satisfies the so-called turnpike property, namely it is exponentially close to the (unique) stationary ergodic state for any proportionally long intermediate time. |
| title | Long time behaviour of Mean Field Games with fractional diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.06183 |