We consider continuous-time Markov branching processes in semi-Markov random environment and obtain diffusion approximation results for the near critical case. The problem of semi-Markov environment, presented here, is new and more interesting than the Markov case, since it includes many particular interesting cases: Markov, renewal, etc. The particular case of the Markov random environment of continuous-time branching process diffusion approximation results are obtained.

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半马尔可夫环境中分支过程的扩散近似

我们考虑了半马尔可夫随机环境中的连续时间马尔可夫分支过程，并获得了近临界情况下的扩散近似结果。这里提出的半马尔可夫环境问题比马尔可夫情况新，而且更有趣，因为它包括许多特殊的情况：马尔可夫，更新等。连续时间分支过程扩散的马尔可夫随机环境的特殊情况得到近似结果。