基于势能级的能量分解
Energy decomposition by potential level
中文总结 AI 辅助
本文研究马尔可夫过程的过剩函数，证明正则狄利克雷空间中函数拟连续版本的局部能量测度性质，并为特定狄利克雷过程建立占有时密度性质。
中文摘要 AI 辅助
第一部分，我们研究沿样本路径为连续半鞅的马尔可夫过程的过剩函数，该性质可由半鞅的局部时理论导出。接下来处理狄利克雷空间情形，证明若u为正则狄利克雷空间中函数u的拟连续版本，则u的局部能量测度在u下的像关于勒贝格测度绝对连续。最后，第三部分中，我们为某些狄利克雷过程建立占有时密度性质。
英文摘要
In the first part we study excessive functions for a Markov process that are continuous semimartingales along the sample paths. The property then follows from the theory of local times of semimartingales. We next treat the case of Dirichlet spaces and show that, if u is a quasi-continuous version of a function u belonging to a regular Dirichlet space, then the image under u of the local energy measure of u is absolutely continuous with respect to Lebesgue measure. Finally, in a third part, we establish the occupation-time density property for certain Dirichlet processes.
