Which Lévy processes satisfy Hunt’s hypothesis (H) is a long-standing open problem in probabilistic potential theory. The study of this problem for one-dimensional Lévy processes suggests us to consider (H) from the point of view of the sum of Lévy processes. In this paper, we present theorems and examples on the validity of (H) for the sum of two independent Lévy processes. We also give a novel condition on the Lévy measure which implies (H) for a large class of one-dimensional Lévy processes.

中文翻译：

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两个独立Lévy过程之和的亨特假设（H）

Lévy过程中哪些满足亨特假设（H）是概率潜能理论中一个长期存在的开放问题。对一维列维过程的这一问题的研究建议我们从列维过程的总和的角度考虑（H）。在本文中，我们针对两个独立的Lévy过程之和给出关于（H）有效性的定理和示例。我们还对Lévy度量给出了一个新颖的条件，该条件暗示了一大类一维Lévy过程的（H）。