论文标题
带有应用的平均元素稳定下属
Average-tempered stable subordinators with applications
论文作者
论文摘要
在本文中，考虑了具有回火稳定分布的下属的运行平均值。我们研究了一个以前未开发的无限活性下属的家族，该家族是由运行平均过程的概率分布引起的，并确定其跳跃强度度量。讨论了包括伽马过程和逆高斯流程在内的特殊情况。然后，我们为分布功能，累积物和力矩提供易于实现的公式，并为其渐近行为提供明确的估计。进行数值实验以说明所提出的公式的适用性和效率。运行平均过程的两个重要范围及其等级分布的下属均通过混凝土应用在结构降解建模和金融衍生品定价中进行了检查，在这些降级建模和金融衍生品定价中，它们相对于几种现有模型的优点都被强调，并提到了Euler Expitization和复合泊松近近似技术。
In this paper the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running average process and determine their jump intensity measures. Special cases including gamma processes and inverse Gaussian processes are discussed. Then we derive easily implementable formulas for the distribution functions, cumulants, and moments, as well as provide explicit estimates for their asymptotic behaviors. Numerical experiments are conducted for illustrating the applicability and efficiency of the proposed formulas. Two important extensions of the running average process and its equi-distributed subordinator are examined with concrete applications to structural degradation modeling and financial derivatives pricing, where their advantages relative to several existing models are highlighted together with the mention of Euler discretization and compound Poisson approximation techniques.
