论文标题
广义量表功能，用于频谱负Lévy过程
Generalized scale functions for spectrally negative Lévy processes
论文作者
论文摘要
对于频谱负的莱维过程，量表功能出现在双面出口问题的解决方案中，尤其是与第一次退出闭合间隔的拉普拉斯变换有关。在本文中，我们考虑了更多一般功能的拉普拉斯变换，这些功能可以同时取决于该过程的值及其上限，直到退出时间。这些数量将以广义量表函数来表示，可以使用偏移理论来定义。在这种情况下，功能不取决于至上，这些量表功能与文献中的功能相吻合，因此这项工作的结果是它们的扩展。
For a spectrally negative Lévy process, scale functions appear in the solution of two-sided exit problems, and in particular in relation with the Laplace transform of the first time it exits a closed interval. In this paper, we consider the Laplace transform of more general functionals, which can depend simultaneously on the values of the process and its supremum up to the exit time. These quantities will be expressed in terms of generalized scale functions, which can be defined using excursion theory. In the case the functional does not depend on the supremum, these scale functions coincide with the ones found on the literature, and therefore the results in this work are an extension of them.
