Abstract In this paper, under the assumption of Holder continuous coefficients, we prove the strong Feller property for the solution to one-dimensional Levy 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.

中文翻译：

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具有 Hölder 连续系数的一维 Lévy 过程的强 Feller 属性驱动随机微分方程

摘要 本文在Holder连续系数的假设下，证明了求解一维Levy过程驱动的随机微分方程的强Feller性质。我们的证明基于 Yamada-Watanabe 逼近技术、Girsanov 定理和耦合方法的工具。使用这种方法，还可以获得相同方程对初始数据的连续依赖性，这是独立的兴趣。