Qiang Li, Yu, A fluctuation type limit theorem for Ji.ina processes with immigration, Acta mathematica Sinica. English series (Print) , 25(8), 2009, pp. 1379-1388
It is proved by the theory of semigroup that the Ornstein-Uhlenbeck type process with jumps can arise from the fluctuation limit of a sequence of Ji.ina processes with immigration under suitable moments conditions.