Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909184036962304 |
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| author | Grube, Sebastian |
| author_facet | Grube, Sebastian |
| contents | We consider a large class of nonlinear FPKEs with coefficients of Nemytskii-type depending explicitly on time and space, for which it is known that there exists a sufficiently Sobolev-regular distributional solution u in L^1 and L^\infty. We show that there exists a unique strong solution to the associated McKean-Vlasov SDE with time marginal law densities u. In particular, every weak solution of this equation with time marginal law densities u can be written as a functional of the driving Brownian motion. Moreover, plugging any Brownian motion into this very functional produces a weak solution with time marginal law densities u. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_09576 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case Grube, Sebastian Probability 60H10, 60G17, 35C99 We consider a large class of nonlinear FPKEs with coefficients of Nemytskii-type depending explicitly on time and space, for which it is known that there exists a sufficiently Sobolev-regular distributional solution u in L^1 and L^\infty. We show that there exists a unique strong solution to the associated McKean-Vlasov SDE with time marginal law densities u. In particular, every weak solution of this equation with time marginal law densities u can be written as a functional of the driving Brownian motion. Moreover, plugging any Brownian motion into this very functional produces a weak solution with time marginal law densities u. |
| title | Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type: the time-dependent case |
| topic | Probability 60H10, 60G17, 35C99 |
| url | https://arxiv.org/abs/2203.09576 |