Moment properties for two-type continuous-state branching processes in random environments

We first derive the recurisions for integer moments of two-type continuous-state branching processes in L\'{e}vy random environments. Result shows that the $n$th moment of the process is a polynomial of the initial value of the process with at most $n$ degree. Under some natural condition, the criteria for the existence of $f$-moment of the process are also proved.