随机环境中受传染性疾病影响的分枝过程的极限性质

Limit properties for branching process affected by communicable diseases in random environments

给出了独立随机环境中受传染性疾病影响的分枝过程{Z_(n),n∈N}的模型,讨论了该模型的极限性质,并给出了分枝过程经{S_(n),n∈N}和{U_(n),n∈N}规范化后{W_(n),n∈N}和{W_(n),n∈N}几乎处处收敛和L^(1)收敛的充分条件,得到{W_(n),n∈N}L^(2)收敛的充分条件和{W_(n),n∈N}极限非退化到0的充分条件和必要条件。

The model of branching process{Z_(n),n∈N}affected by communicable diseases in independent random environment is proposed,and the limit properties of this model are discussed.Under the normalization factors{S_(n),n∈N}and{U_(n),n∈N},the normalization processes{W_(n),n∈N}and{W_(n),n∈N}are studied,the sufficient conditions of{W_(n),n∈N}and{W_(n),n∈N}a.s.and L^(1) convergence are given;the sufficient condition of{W_(n),n∈N}L^(2) convergence,a sufficient condition and a necessary condition for the limit of{W_(n),n∈N}converging to a non-degenerate at 0 random variable are obtained.