Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria
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| Format: | Preprint |
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2025
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| _version_ | 1866911472591831040 |
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| author | Shaposhnikov, Stanislav V. Shatilovich, Dmitry V. |
| author_facet | Shaposhnikov, Stanislav V. Shatilovich, Dmitry V. |
| contents | We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of doubling variables and a~priory estimates with Lyapunov functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria Shaposhnikov, Stanislav V. Shatilovich, Dmitry V. Analysis of PDEs Optimization and Control Probability 35K55, 35Q89, 49N80 We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of doubling variables and a~priory estimates with Lyapunov functions. |
| title | Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria |
| topic | Analysis of PDEs Optimization and Control Probability 35K55, 35Q89, 49N80 |
| url | https://arxiv.org/abs/2508.15029 |