论文标题
在lévy过程中的比例功能，具有负相类型的跳跃
On scale functions for Lévy processes with negative phase-type jumps
论文作者
论文摘要
我们为Lévy过程提供了量表函数的新表达，并具有负相类型的跳跃。它是根据特定的过渡速率矩阵，该矩阵明确至单个正数。提出了用于计算后者的单调迭代方案，并表明误差呈指数速度衰减。我们的数值示例表明，该算法允许使用一百个阶段使用相型分布，这在使用根部的刻度函数的已知公式时是有问题的。可以预料到其他分布的扩展，例如矩阵 - 指数和无限差相类型。
We provide a novel expression of the scale function for a Lévy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for the calculation of the latter is presented and it is shown that the error decays exponentially fast. Our numerical examples suggest that this algorithm allows to employ phase-type distributions with a hundred of phases, which is problematic when using the known formula for the scale function in terms of roots. Extensions to other distributions, such as matrix-exponential and infinite-dimensional phase-type, can be anticipated.
