论文标题
在不同环境中具有渐近恒定均值矩阵的两种线性分支分支过程
Two-type linear fractional branching processes in varying environments with asymptotically constant mean matrices
论文作者
论文摘要
考虑具有渐近恒定均值矩阵的不同环境中的两种线性分支分支过程。令$ν$为灭绝时间。在某些条件下，我们表明$ p（ν= n）$和$ p（ν> n）$均与平均矩阵光谱半径的某些功能相同。我们还举例说明了$ p（ν= n）$以各种速度衰减，例如$ \ frac {c} {n（\ log n）^2}，$ $ \ frac {c} {c} {n^β}，β> 1 $ et al。这与均质的多元沃尔顿 - 瓦特森过程大不相同。
Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let $ν$ be the extinction time. Under certain conditions, we show that both $P(ν=n)$ and $P(ν>n)$ are asymptotically the same as some functions of the products of spectral radii of the mean matrices. We also give an example for which $P(ν=n)$ decays with various speeds such as $\frac{c}{n(\log n)^2},$ $\frac{c}{n^β},β>1$ et al. which are very different from the ones of homogeneous multitype Galton-Watson processes.
