随机环境下依人口数控制两性分枝过程的极限行为

考虑独立同分布环境下依人口数控制两性分枝过程,其中后代概率分布受一个随机环境过程影响,配对函数依赖人口数,参与繁衍后代的配对单元数又受控制函数约束。讨论了当k→∞时,均值rk,θ趋于极限rθ1(rk,θ是繁衍分布的均值),得出了模型的一些概率性质以及Wn依L1收敛的必要条件。

Limit Behaviour for Controlled Bisexual Branching Processes with Population Size-dependent Mating in Random Environments

We consider controlled bisexual branching processes with population-size-dependent mating, where the independently identically distributed random environments affect the law of offspring distribution, the mating function depends on population size,and the controlled function constrains the matching units. We investigate the case when r_(k,θ), the means of the offspring, tends to a limit r_θ>1 as k→∞, and obtain some probability properties such as the necessary condition for convergence of W_n in L~1 .