分枝Q过程的一个特征

A Charcateristic Property of Branching Process

设Ｅ＝｛０，１，２，…），Ｑ为Ｅ上的全稳定Ｑ─矩阵，众所周知，如果Ｑ是分枝Ｑ─矩阵，则最小Ｑ过程Ｐ（ｔ）＝（ｐｉｊ（ｔ））满足： 本文证明了Ｅ上任意一个全稳定Ｑ过程Ｐ（ｔ）＝（ｐｉｊ（ｔ））如果满足上式及对某个 则其Ｑ矩阵必为分板Ｑ─矩阵，且该过程就是最小Ｑ过程．

Let E= {0, 1, 2, ... } and Q be a Branching Q-matrix then the minimal Q process P (t ) = (pij (t ); i,j ∈ E ) satisfies In this paper,we have obtained that,for any stable Q process P(t)satisfying above formula and for some t > 0, its Q-matrix must be a Branching Q -matrix,and P(t) must be the minimal Q process.