谱负lsamvy过程的q尺度函数

Pub Date : 2021-09-20 DOI:10.1017/apr.2022.10

Anita Behme, David Oechsler, R. Schilling

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引用次数: 1

摘要

摘要我们得到了任意谱负Lévy过程（包括具有无限跳跃活动的过程）的q标度函数的级数展开式，并用这些级数展开式导出了显式q标度功能的各种新例子。此外，我们还研究了具有无穷跳跃活动的谱负Lévy过程的q尺度函数的光滑性。这补充了Chan等人（Prob.Theory Relat.Fields 1502011）关于具有高斯分量或有界变化的谱负Lévy过程的先前结果。

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On q-scale functions of spectrally negative Lévy processes

Abstract We obtain series expansions of the q-scale functions of arbitrary spectrally negative Lévy processes, including processes with infinite jump activity, and use these to derive various new examples of explicit q-scale functions. Moreover, we study smoothness properties of the q-scale functions of spectrally negative Lévy processes with infinite jump activity. This complements previous results of Chan et al. (Prob. Theory Relat. Fields 150, 2011) for spectrally negative Lévy processes with Gaussian component or bounded variation.

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