We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuous-state branching processes with immigration and Ornstein--Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.
"Affine processes and applications in finance." Ann. Appl. Probab. 13 (3) 984 - 1053, August 2003. https://doi.org/10.1214/aoap/1060202833