Large Deviations Principle for SDEs with Dini Continuous Drifts

In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and result are new in related fields. Moreover, the result is also extended to a class of degenerate stochastic differential equations with Dini continuous drifts.