论文标题
在$ q $ - 尺度的功能上的频谱负面复合泊松过程
On $q$-scale functions of spectrally negative compound Poisson processes
论文作者
论文摘要
量表功能在频谱负Lévy过程的波动理论中起着核心作用。对于具有积极漂移的频谱负复合泊松过程，从该过程的特征方面，$ q $ scale函数的新表示。此外，提出了类似的衍生物和$ q $ scale功能的原始形式。获得的衍生产品的公式允许完全曝光所考虑的$ q $ scale功能的平滑度。给出了一些$ q $ scale功能的明确示例以进行插图。
Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes. For spectrally negative compound Poisson processes with positive drift, a new representation of the $q$-scale functions in terms of the characteristics of the process is derived. Moreover, similar representations of the derivatives and the primitives of the $q$-scale functions are presented. The obtained formulae for the derivatives allow for a complete exposure of the smoothness properties of the considered $q$-scale functions. Some explicit examples of $q$-scale functions are given for illustration.
