Polynomial McKean-Vlasov SDEs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910846248026112 |
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| author | Cuchiero, Christa Möller, Janka |
| author_facet | Cuchiero, Christa Möller, Janka |
| contents | We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the state variables themselves as well as their conditional moments in a way that mimics the standard polynomial structure. Our approach leads to new results on the existence and uniqueness of solutions to such conditional McKean-Vlasov SDEs which are, to the best of our knowledge, not obtainable using standard methods. Moreover, we show in the case without common noise that the moments of these McKean-Vlasov SDEs can be computed by non-linear ODEs. As a by-product, this also yields new results on the existence and uniqueness of global solutions to certain ODEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial McKean-Vlasov SDEs Cuchiero, Christa Möller, Janka Probability 60H10, 60J25, 34A34 We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the state variables themselves as well as their conditional moments in a way that mimics the standard polynomial structure. Our approach leads to new results on the existence and uniqueness of solutions to such conditional McKean-Vlasov SDEs which are, to the best of our knowledge, not obtainable using standard methods. Moreover, we show in the case without common noise that the moments of these McKean-Vlasov SDEs can be computed by non-linear ODEs. As a by-product, this also yields new results on the existence and uniqueness of global solutions to certain ODEs. |
| title | Polynomial McKean-Vlasov SDEs |
| topic | Probability 60H10, 60J25, 34A34 |
| url | https://arxiv.org/abs/2502.19203 |