A Zvonkin's transformation for stochastic differential equations with singular drift and applications
A Zvonkin's transformation for stochastic differential equations with singular drift and applications
复制标题
具有奇异漂移的随机微分方程的Zvonkin变换及其应用
DOI：
10.1016/j.jde.2021.06.031
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Yuan Chenggui
中科院分区：
文献类型：
--
作者：
Zhang Shao-Qin;Yuan Chenggui
本文通过建立带奇异项和Lipschitz项的抛物型偏微分方程的局部Lp-Lq估计和Sobolev估计，给出了带奇异项和Lipschitz漂移的随机微分方程的一个新的Zvonkin型变换.建立了相应的Krylov估计。作为应用，在没有正则性假设的情况下，建立了具有Hölder连续扩散系数和奇异漂移项的随机方程的无量纲Harnack不等式.
In this paper, by establishing the localized L p-L q estimate and Sobolev estimates for parabolic partial differential equations with a singular first order term and a Lipschitz first order term, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts. The associated Krylov's estimate is established. As applications, dimension-free Harnack inequalities are established for stochastic equations with Hölder continuous diffusion coefficient and singular drift term without regularity assumption.