独立同分布随机环境上临界两性分枝过程的灭绝概率渐近行为

Asymptotic Behavior of the Extinction Probability in Supercritical Bisexual Branching Processes with Independent and Identically Distributed Random Environments

给出了初值为N的独立同分布(i.i.d)随机环境上临界两性分枝过程灭绝概率的渐近上、下界。即当N充分大时,存在0<α1,α2<+∞,0<C1,C2<+∞,使有C1N-α1≤qN≤C2N-α2.

In the supercritical amphoteric branching processes with independent and identically distributed random environments, it is shown that, under the some conditions, there exist constants 0〈α1,α2〈＋∞,0〈C1,C2〈＋∞,such that the extinction probability starting with N individuals is bounded below by C1N-α1,and above by C2N^α2 for sufficiently large N.