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

Abstract

In this paper, by establishing the $L^p$-$L^q$ 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, Harnack inequalities are established for stochastic equations with Hölder continuous diffusion coefficient and singular drift term without regularity assumption.

arXiv comment38

References in corpus (4)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
• Ergodicity of stochastic differential equations with jumps and singular coefficients
• Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature

Cited by in corpus (4)

• McKean-Vlasov SDEs with Drifts Discontinuous under Wasserstein Distance
• Distribution Dependent Reflecting Stochastic Differential Equations
• Derivative Formula for Singular McKean-Vlasov SDEs
• Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs