H?lder continuity property of the densities of SDEs with singular drift coefficients

摘要

We prove that the solution of stochastic differential equations with deterministic diffusion coefficient admits a H?lder continuous density via a condition on the integrability of the Fourier transform of the drift coefficient.?In our result, the integrability is an important factor to determine the order of H?lder continuity of the density. Explicit examples and some applications are given.