A Zvonkin's transformation for stochastic differential equations with singular drift and applications

[摘要] 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 Holder continuous diffusion coefficient and singular drift term without regularity assumption. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-05

[关键词] Zvonkin's transformation;Singular diffusion processes;Krylov's estimate;Harnack inequality