标题： 首次通过时间问题中生存概率的Sturm-Liouville系统 显示英文标题

标题： Sturm-Liouville systems for the survival probability in first-passage time problems

摘要： 我们推导出一个斯特姆-刘维尔方程组，用于首次通过时间问题中生存概率的精确计算。 该方程组是与从随机游走理论中得到的维纳-霍普夫积分方程相关的。 所推导的方法是对现有文献的一种替代方法，并我们在一个易于处理但有意义的例子中将其与离散时间和连续时间随机游走的直接计算进行了对比。 在这一框架下，Sparre Andersen定理被证明是该系统的一个边界条件。 显示英文摘要

摘要： We derive a Sturm-Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener-Hopf integral equation obtained from the theory of random walks. The derived approach is an alternative to the existing literature and we tested it against direct calculations from both discrete- and continuous-time random walks in a manageable, but meaningful, example. Within this framework, the Sparre Andersen theorem results to be a boundary condition for the system.