满足Cramér条件的Lévy过程的泛函极限定理
Functional limit theorems for Lévy processes satisfying Cramér's condition
摘要：
我们考虑一个从$x<0$开始的Lévy过程，其条件是有一个正的最大值。当Cramér条件成立时，我们分别给出了（双侧）路径在进入$(0,\infty)$的第一瞬间移动和在达到其最大值的瞬间移动的规律的两个弱极限定理作为$x\to -\infty$.这两个渐近结果的比较产生了一些有趣的身份有关的时间反演，保险风险，自相似马尔可夫过程。
英文摘要：
We consider a Lévy process that starts from $x<0$ and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the first instant when it enters $(0,\infty)$, respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.
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