Hunt’s hypothesis (H) and the related Getoor’s conjecture is one of the most important problems in the basic theory of Markov processes. In this paper, we investigate the invariance of Hunt’s hypothesis (H) for Markov processes under two classes of transformations, which are change of measure and subordination. Our first theorem shows that for two standard processes (X_t) and (Y_t), if (X_t) satisfies (H) and (Y_t) is locally absolutely continuous with respect to (X_t), then (Y_t) satisfies (H). Our second theorem shows that a standard process (X_t) satisfies (H) if and only if \((X_{\tau _{t}})\) satisfies (H) for some (and hence any) subordinator (τ_t) which is independent of (X_t) and has a positive drift coefficient. Applications of the two theorems are given.

亨特的假设（H）和相关的盖图猜想是马尔可夫过程基本理论中最重要的问题之一。在本文中，我们研究了马尔可夫过程的亨特假设（H）在两类转换下的不变性，即变换和度量从属。我们的第一个定理表明，对于两个标准过程（X _t）和（Y _t），如果（X _t）满足（H）且（Y _t）相对于（X _t）局部绝对连续，则（Y _t）满足（H）。我们的第二个定理表明一个标准过程（X _t）满足（H）当且仅当\（（X _ {\ tau蛋白_ {吨}}）\）满足（H）的一些（因此任何）从属连词（τ_吨），其是独立的（X_吨），并且具有正漂移系数。给出了两个定理的应用。