有恢复的生成分支过程的Feller性质(英文)

The Feller Property for Generalized Branching Processes with Resurrection

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θ是分支q矩阵中的非线性数, 总是存在一个分点θ0满足1 ≤θ0 ≤ 2或θ0 < +∞使得生成分支过程是否是Feller的要依据θ < θ0或者θ > θ0.

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 θ0 with 1 ≤ θ0 ≤ 2 or θ0 ＋∞ such that whether the generalized branching processes（with resurrection） are Feller processes or not according to θ θ0 or θ θ0,where θ is the nonlinear number given in the branching q-matrix.