Strong Feller property for one-dimensional Lévy processes driven stochastic differential equations with Hölder continuous coefficients

Abstract

In this paper, under the assumption of Hölder continuous coefficients, we prove the strong Feller property for the solution to one-dimensional Lévy processes driven stochastic differential equations. Our proof is based on the tools of Yamada–Watanabe approximation technique, Girsanov’s theorem and coupling method. Using this approach, the continuous dependence on initial data for the same equations can be also obtained, which is of independent interest.