The limit theorem is the theoretical basis of mathematical statistics and error analysis,and the theoretical expla-nation of the new limit theorem in practical application has been produced constantly,which promotes the development of proba-bility theory. In branching process of the random environment,when the expectation of the environment changes and variance are limited,the new explanation of limit theorem and large deviation theorem for environment first-arrival is put forward.%极限定理是数理统计学及误差分析的理论基础,在实际应用中,新的极限定理理论解释不断产生,推动了概率论的发展.在随机环境的分枝过程中,当环境变化的期望值以及方差有限时,给出了环境首达时的极限定理及大偏差定理新解.
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