中文摘要：

考虑了带有随机控制函数的人口数相依的受控分枝过程．在对后代分布及控制函数的适当假设下，给出了过程是否以概率1 灭绝的判定准则并建立了适当的规范化序列几乎处处收敛的充分性条件．

英文摘要：

In this paper, popuplation-size-dependent controlled branching processes with random control functions is investigated. Under suitable assumptions on the offspring distribution and control function, a criterion is given to identify whether or not the process admits ultimate extinct with probability one and sufficient conditions on almost sure convergence for the suitably normed sequence are established.