Information geometry of tempered stable processes

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.