一致突变人口半群的渐近行为

Asymptotic Behaviour of the Population Semigroups with Uniform Catastrophes

证明了一致突变人口矩阵Q在l∞上生成一个正压缩积分半群T(t)且该压缩积分半群T(t)是随机单调的.讨论了压缩积分半群T(t)关于状态i及时间t的渐近行为,证明了一致突变人口过程具有强遍历性.

In this paper, we show that the uniform catastrophe population q-matrix Q generates a postive contraction integrated semigroup T（t） on l∞. T（t） is stochastically monotone and its limit behaviour as state i tends to infinity is discussed. We also prove that the process is always strongly ergodic.