对于一个好的马氏过程X=(X_t)，Hunt假设(H)说的是：X的半极集都是X的极集。此假设在马氏过程的位势理论中具有重要作用。大约45年前，加州大学圣地亚哥分校（UCSD）的Getoor教授猜测：除了像一致运动那样极端不对称情形外所有的Levy过程都满足Hunt假设(H)。我们从2010年开始研究这个问题，取得了一些成果，发表了三篇学术论文。但是到目前为止，距离完全理解Getoor猜测还有很远的路要走。 本项目拟继续研究Levy过程的Hunt假设(H)。 另外，鉴于随机微分方程的广泛性和重要性，本项目还将研究随机微分方程的解过程在什么条件下满足Hunt假设(H)，为随机微分方程的解过程的位势理论作出贡献。

For a nice Markov process X=(X_t), Hunt's hypothesis (H) says that any semi-polar set of X is polar for X. This hypothesis plays an important role in the potential theory of Markov processes. About 45 years ago, Professor Getoor of UCSD conjectured that essentially all Levy processes satisfy Hunt's hypothesis (H) except some extremely non-symmetric cases like uniform motion. In 2010, we started to study this problem, obtained some results, and published three papers. But up to now, there is still a far way to completely understanding Getoor's conjecture. This grant will continue to study Hunt's hypothesis (H) for Levy processes. In addition, in view of universality and importance of stochastic differential equations (SDEs), we will also study Hunt's hypothesis (H) for the Markov processes induced by SDEs, and wish to make contribution to the potential theory of the solution processes associated with SDEs.