%0 Journal Article %A Zhang Xiuzhen %A Li Yangrong %T The Feller Property for Generalized Branching Processes with Resurrection %D 2011 %R %J CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS %P 48-60 %V 27 %N 1 %X

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

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