有恢复的生成分支过程的Feller性质
The Feller Property for Generalized Branching Processes with Resurrection
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摘要: 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.Abstract: 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