Information geometry of tempered stable processes

We find the information geometry of tempered stable processes. Beginning with the derivation of $\alpha$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $\alpha$-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.