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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2502.13353 |
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| _version_ | 1866916839650492416 |
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| author | Wang, Feng-Yu Yuan, Chenggui Zhao, Xiao-Yu |
| author_facet | Wang, Feng-Yu Yuan, Chenggui Zhao, Xiao-Yu |
| contents | We consider stochastic differential equations on $\mathbb R^d$ with coefficients depending on the path and distribution for the whole history. Under a local integrability condition on the time-spatial singular drift, the well-posedness and Lipschitz continuity in initial values are proved, which is new even in the distribution independent case. Moreover, under a monotone condition, the asymptotic log-Harnack inequality is established, which extends the corresponding result of [5] derived in the distribution independent case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path-Distribution Dependent SDEs: Well-Posedness and Asymptotic Log-Harnack Inequality Wang, Feng-Yu Yuan, Chenggui Zhao, Xiao-Yu Probability 60H10, 60J60, 47G20 We consider stochastic differential equations on $\mathbb R^d$ with coefficients depending on the path and distribution for the whole history. Under a local integrability condition on the time-spatial singular drift, the well-posedness and Lipschitz continuity in initial values are proved, which is new even in the distribution independent case. Moreover, under a monotone condition, the asymptotic log-Harnack inequality is established, which extends the corresponding result of [5] derived in the distribution independent case. |
| title | Path-Distribution Dependent SDEs: Well-Posedness and Asymptotic Log-Harnack Inequality |
| topic | Probability 60H10, 60J60, 47G20 |
| url | https://arxiv.org/abs/2502.13353 |