�лָ������ɷ�֧���̵�Feller����

首先, 当$Q$是一个拟单调的q矩阵的时候, 我们找出最小的$Q$函数是一个Feller的转移函数的准则. 然后我们把这个结论应用于生成分支q矩阵并得到相应的生成分支过程的Feller准则. 特别地, 设$\theta$是分支q矩阵中的非线性数, 总是存在一个分点$\theta_0$满足$1\leq\theta_0\leq2$或$\theta_0<+\infty$使得 生成分支过程是否是Feller的要依据$\theta<\theta_0$或者$\theta>\theta_0$.

The Feller Property for Generalized Branching Processes with Resurrection

We first establish a criterion for the minimal $Q$-function to be a Feller transition function when $Q$ is a quasi-monotone q-matrix. We then apply this result to generalized branching q-matrices and obtain the corresponding Feller criteria for generalized branching processes. In particular, it is shown that there always exists a separating point $\theta_0$ with $1\leq\theta_0\leq2$ or $\theta_0<+\infty$ such that whether the generalized branching processes (with resurrection) are Feller processes or not according to $\theta<\theta_0$ or $\theta>\theta_0$, where $\theta$ is the nonlinear number given in the branching q-matrix