独立同分布随机环境中两性Galton-Watson分支过程灭绝概率的渐近行为

The Asymptotic Behaviour of the Extinction Probabibity in Bisexual Galton-Watson Branching Processes with Independent and Identically Distributed Random Environments

摘要: 本文研究了独立同分布随机环境中的两性Galton-Watson分支过程, 在上临界情形下, 当k充分大时, q_k\leq ck^-\alpha.

Abstract: In bisexual Galton-Watson branching process with independent and identically distributed random environments, it is shown that under certain conditions there exists 0<\alpha<+\infty and 0<c<+\infty such that the extinction probability starting with k individuals is bounded above by ck^-\alpha for sufficiently large k.