A limit theorem of two-type Galton–Watson branching processes with immigration

We provide a simple set of sufficient conditions for the weak convergence of two-type Galton–Watson branching processes with immigration to two-dimensional, continuous-time, continuous-state branching processes with immigration, which generalizes the limit result of Li [Li, Z.H., 2006a. A limit theorem of discrete Galton–Watson branching processes with immigration. J. Appl. Probab. 43, 289–295].