随机环境中受控分枝过程的极限定理

Limit Theorems for Controlled Branching Processes in Random Environments

讨论了随机环境中受控分枝过程{Zn：n∈N}的极限问题.给出了过程在{Sn：n∈N}下的规范化过程{Wn：n∈N}几乎处处收敛、L-1收敛和L-2收敛的充分条件,以及过程{W：n∈N}的极限非退化于0的充分条件和必要条件,得到了过程在{In：n∈N}下的规范化过程{Wn：n∈N}几乎处处收敛和L-1收敛的充分条件.

The limiting behaviors for controlled branching processes in random environments are discussed. Under the normalization factor {Sn ： n∈ N}, the normalization processes {Wn ： n∈N} of are studied, and the sufficient conditions of{Wn： n ∈ N} a.s., L^1 and L^2 convergence are given; A sufficient condition and a necessary condition for convergence to a non-degenerate at 0 random variable are got; Under the normalization factor {In ： n ∈ N}, the normalization processes {Wn ： n ∈ N} are discussed, and the sufficient conditions of {Wn ： n ∈ N} a.s., and L1 convergence are obtained.