Regularity Estimates for Singular Density Dependent SDEs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910199897391104 |
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| author | Wang, Feng-Yu Wen, Qiumiao Yang, Fen-Fen |
| author_facet | Wang, Feng-Yu Wen, Qiumiao Yang, Fen-Fen |
| contents | Consider the density dependent (i.e. Nemytskii-type) SDEs on $\mathbb R^d$, where the drift $b_t(x,ρ(x),ρ)$ is locally integrable in $(t,x)\in [0,\infty)\times \mathbb R^d$ and may be singular in the distribution density function $ρ$. The relative/Renyi entropies between two time-marginal distributions are estimated by using the Wasserstein distance of initial distributions. When $d=1$ and $b_t$ decays at $t=0$ with rate $t^{\frac 1 2+}$, our the relative entropy estimate coincides with the classical entropy-cost inequality for elliptic diffusion processes. To estimate the Renyi entropy, a refined Khasminskii estimate is presented for singular SDEs which may be interesting by itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05634 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity Estimates for Singular Density Dependent SDEs Wang, Feng-Yu Wen, Qiumiao Yang, Fen-Fen Probability Consider the density dependent (i.e. Nemytskii-type) SDEs on $\mathbb R^d$, where the drift $b_t(x,ρ(x),ρ)$ is locally integrable in $(t,x)\in [0,\infty)\times \mathbb R^d$ and may be singular in the distribution density function $ρ$. The relative/Renyi entropies between two time-marginal distributions are estimated by using the Wasserstein distance of initial distributions. When $d=1$ and $b_t$ decays at $t=0$ with rate $t^{\frac 1 2+}$, our the relative entropy estimate coincides with the classical entropy-cost inequality for elliptic diffusion processes. To estimate the Renyi entropy, a refined Khasminskii estimate is presented for singular SDEs which may be interesting by itself. |
| title | Regularity Estimates for Singular Density Dependent SDEs |
| topic | Probability |
| url | https://arxiv.org/abs/2602.05634 |