Moment Properties for Two-type Continuous-state Branching Processes in L\'evy Random Environments
Chen Shukai , Zheng Xiangqi
2023, v.29, Issue 3, 301-328
ABSTRACT
We first derive the recursions for integer moments of two-type cont\-in\-uous-state branching processes in L\'{e}vy random environments. We show that the $n$th moment of the process is a polynomial of the initial value of the process with at most $n$ degree. Meanwhile, the criteria for the existence of $f$-moment of the process is also established under some natural conditions.
Keywords: Moment property, continuous-state branching process, random environment
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