论文标题
关于扩散过程的强伐属属性的注释
A note on the strong Feller property of diffusion processes
论文作者
论文摘要
在本说明中，我们证明了强大的Markov准扩散过程的强大特性，其对应于具有仅有限的可测量系数的椭圆算子。我们还证明了与准扩散过程和Harnack不平等相关的谐波功能的Hölder连续性。作为一种应用，我们表明，对于这种扩散过程，常规边界点的概率定义与“分析”一个相吻合。 这些结果的抛物线也对应物。证明是\ cite {krs_79}和\ cite {kr_18}的参数的改编。
In this note we prove the strong Feller property of a strong Markov quasi diffusion process corresponding to an elliptic operator with merely bounded measurable coefficients. We also prove Hölder continuity of harmonic functions associated with the quasi diffusion process and Harnack inequality. As an application, we show that for such diffusion processes the probabilistic definition of a regular boundary point coincides with the 'analytic' one. The parabolic counterparts of these results are presented as well. The proofs are adaptations of arguments from \cite{KrS_79} and \cite{Kr_18}.
