In this paper, under the assumption of Hölder continuous coefficients, we prove the strong Feller property and continuous dependence on initial data for the solution to one-dimensional stochastic differential equations whose proof are based on the technique of local time, coupling method and Girsanov’s transform.
"Strong Feller property and continuous dependence on initial data for one-dimensional stochastic differential equations with Hölder continuous coefficients." Electron. Commun. Probab. 25 1 - 10, 2020. https://doi.org/10.1214/20-ECP284