Central Limit Theorem for a Class of Super \alpha-Symmetric Stable Processes with Immigration

In this paper, we prove two central limit theorems for a class of super \alpha-symmetric stable processes with immigration and its occupation time processes, where the immigration is determined by the Lebesgue measure \lambda. The distributions of their renormalized processes converge as t\to+\infty to those of centered Gaussian variables in \mathcalS'(\mathbbR^d).