Moment formulas for multi-type continuous state and continuous time   branching processes with immigration
  Recursions for moments of multi-type continuous state and continuous time branching process with immigration are derived. It turns out that the $k$-th (mixed) moments and the $k$-th (mixed) central moments are polynomials of the initial value of the process, and their degree are at most $k$ and $\lfloor k/2 \rfloor$, respectively. 
Matyas Barczy, Zenghu Li, Gyula Pap
math.PR