For a positive continuous function f satisfying some standard conditions, we study the f -moments of continuous-state branching processes with or without immigration. The main results give criteria for the existence of the f -moments. The characterization of the processes in terms of stochastic equations plays an essential role in the proofs.

中文翻译：

---

有或没有移民的连续状态分支过程的时刻

对于满足一些标准条件的正连续函数 f，我们研究了有或没有移民的连续状态分支过程的 f 矩。主要结果给出了 f 矩存在的标准。根据随机方程对过程进行表征在证明中起着至关重要的作用。