条件扩散过程的0-1律与极小调和函数

Zero-One Law for Conditioned Processes and Minimal Harmonic Functions

没(X_t)_(t≥0)是R^d内由散度形式的二阶椭圆算子L决定的扩散过程,(X_t^h)_(t≥0)是其条件扩散过程,其中h>0为有界的Lipschitz区域D内的L-调和函数,本文给出了一个关于(X_t^h)_(t≥0)的0-1律,详细讨论了0-1律,极小调和函数及首中点分布密度函数之间的关系,最后给出了0-1律的—个应用。

Let (Xt)t≥0 be a diffusion process with infinitesimal generator L, (Xth)t≥0 is the conditional process with respect to (Xh ) t≥0 . In this paper, we give a zero-one law for the conditional precess (Xt )t≥0 and discuss the relation among the zero-one law, minimal harmonic function and first hitting density function for (Xt )t≥0 in a bounded Lipschitz domain in detail.