论文标题
自由概率完全随机的措施和莱维基地
Completely Random Measures and Lévy Bases in Free probability
论文作者
论文摘要
本文在自由概率的框架中开发了一种完全随机度量的理论。建立了自由完全随机措施的一般存在结果，并且类似于金曼的经典作品，证明可以将这种随机度量分解为纯原子部分的总和，而（自由）无限划分的部分。根据自由lévy-khintchine表示，对后一部分（称为自由的基础）进行了详细的研究，并与Rajput和Rosinski的经典作品相似的理论进行了详细的研究。最后，建立了一般自由lévy基地的莱维 - itô型分解。
This paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved that such random measures can be decomposed into the sum of a purely atomic part and a (freely) infinitely divisible part. The latter part (termed a free Lévy basis) is studied in detail in terms of the free Lévy-Khintchine representation and a theory parallel to the classical work of Rajput and Rosinski is developed. Finally a Lévy-Itô type decomposition for general free Lévy bases is established.
