论文标题
恢复稳定的分布和有限变化Ornstein-Uhlenbeck过程
Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes
论文作者
论文摘要
构建\ Levy驱动的Ornstein-uhlenbeck过程是与自我分配性概念密切相关的一项任务。特别是，他们的过渡法与以后将被称为其自我兼容的固定法律的\ emph {a-reminder}的属性有关。在本研究中，我们充分表征了这些A-Reminder s的Lévy三胞胎，并提供了一个通用框架来推断有限变化的Ornstein-Uhlenbeck过程的过渡定律，与稳定的稳定分布相关。我们最终将重点放在指数调制的稳定稳定定律的子类上，并得出了与此类分布相关的Ornstein-Uhlenbeck过程的精确生成的算法，其进一步的优势是，在现有文献中采用了一项程序在计算上的效率更高。
Constructing \Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the \emph{a-reminder} of their self-decomposable stationary laws. In the present study we fully characterize the Lévy triplet of these a-reminder s and we provide a general framework to deduce the transition laws of the finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein-Uhlenbeck processes related to such distributions, with the further advantage of adopting a procedure computationally more efficient than those already available in the existing literature.
