标题： 一般Lévy过程的逗留时间 显示英文标题

标题： Occupation times of general Lévy processes

摘要： 对于任意一个不是复合泊松过程的 Lévy 过程$X$，我们对其占用时间感兴趣。 我们采用了一种相当新颖且有用的方法来推导出$X$及其占用时间联合分布的拉普拉斯变换公式。 我们的公式简洁紧凑，更重要的是，公式的结构清楚地展示了计算$X$占用时间的关键量。 相信我们的结果不仅对随机过程的研究具有重要意义，而且对金融应用也至关重要。 显示英文摘要

摘要： For an arbitrary L\'evy process $X$ which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of $X$ and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of $X$. It is believed that our results are important not only for the study of stochastic processes, but also for financial applications.