We find the information geometry of tempered stable processes. Beginning with the derivation of $α$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $α$-connections on their statistical manifolds. Furthermore, we explore statistical applications of this geometric framework. Various tempered stable processes such as generalized tempered stable processes, classical tempered stable processes, and rapidly-decreasing tempered stable processes are presented as illustrative examples.

翻译：本文研究了调和平稳过程的信息几何结构。首先推导了两个调和平稳过程之间的$α$-散度，进而获得了相应统计流形上的Fisher信息矩阵与$α$-联络。此外，我们探讨了该几何框架在统计学中的应用。通过广义调和平稳过程、经典调和平稳过程以及快速衰减调和平稳过程等具体实例，展示了该理论框架的适用性。