线性调控分枝过程的若干结果

Some Results About the Linear Controlled Branching Processes

本文给出了调控函数 φ(x) =kx+b的在零点停止的线性调控分枝过程的增殖速度 ,证明了过程的不稳定性 ,得到了当b =0时成员总数wn 的概率母函数所满足的方程 .

In this paper,the proliferation rate of the linear controlled branching processes stopped at zero in which control function is φ(x)=kx+b are investigated.We have proved instability of the processes.For b=0,the equation about probability generating function of the total number w n of the members is given.