We find information geometry of tempered stable processes. Starting with the derivation of $\alpha$-divergence between two tempered stable processes, Fisher information matrices of tempered stable processes and $\alpha$-connections of their statistical manifolds are obtained. Additionally, we also provide statistical applications for the information geometry of tempered stable processes. Various tempered stable processes such as generalized tempered stable processes, classical tempered stable processes, and rapidly decreasing tempered stable processes are given as examples.

翻译：本文研究了调和稳定过程的信息几何。首先推导了两个调和稳定过程之间的$\alpha$-散度，进而获得了调和稳定过程的费希尔信息矩阵及其统计流形的$\alpha$-联络。此外，我们还提供了调和稳定过程信息几何的统计应用。文中以广义调和稳定过程、经典调和稳定过程及快速衰减调和稳定过程等多种调和稳定过程作为示例进行说明。