Mean field games with common noise and degenerate idiosyncratic noise
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910779782987776 |
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| author | Cardaliaguet, Pierre Seeger, Benjamin Souganidis, Panagiotis |
| author_facet | Cardaliaguet, Pierre Seeger, Benjamin Souganidis, Panagiotis |
| contents | We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10209 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mean field games with common noise and degenerate idiosyncratic noise Cardaliaguet, Pierre Seeger, Benjamin Souganidis, Panagiotis Analysis of PDEs Probability We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system. |
| title | Mean field games with common noise and degenerate idiosyncratic noise |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2207.10209 |