论文标题
稳定过程的关节密度及其至上：规律性和上限
Joint density of a stable process and its supremum: regularity and upper bounds
论文作者
论文摘要
本文结合了三种从模拟的想法的组合，以建立一个几乎最佳的多项式上限，以在稳定过程的关节密度及其在固定时间的全部支持下的固定时间内为关节定律的全部支持。稳定过程的凹室的表示和稳定法律的Chambers-Mallows-stuck表示形式用于定义感兴趣的随机向量的近似值。使用多级蒙特卡洛进行插值技术来加速近似，从而使我们能够建立关节密度的无限可不同性，以及几乎最佳的多项式上限，用于任何顺序的关节混合衍生物。
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated supremum at a fixed time on the entire support of the joint law. The representation of the concave majorant of the stable process and the Chambers-Mallows-Stuck representation for stable laws are used to define an approximation of the random vector of interest. An interpolation technique using multilevel Monte Carlo is applied to accelerate the approximation, allowing us to establish the infinite differentiability of the joint density as well as nearly optimal polynomial upper bounds for the joint mixed derivatives of any order.
