球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。

THE MEASURE-VALUED BRANCHING PROCESSES UNDER THE ACTION OF THE SPHERICAL MEDIUM

We consider a particle system on Rd, when each particle of which is acted by the medium diffused in a (d-l)-dimensional sphere, then it splits and generates new particles,and the new one continues to migrate according to the original rule. With a reasonable hypothesis and a limit procedure the random distribution of the particles at certain time can be described by a measure-valued branching process. The present paper mainly approach involves the asymptotic behaviors of this measure-valued branching process, and further the absolute continuity for its state at certain time is also demonstrated.