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Main Authors: Wang, Feng-Yu, Wen, Qiumiao, Yang, Fen-Fen
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2602.05634
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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