We focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.

中文翻译：

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由具有马尔可夫切换的截断稳定过程驱动的种群动态

我们专注于由两类截断的人口动态$\阿尔法$- 带有马尔可夫切换的稳定过程。为所提出的模型的遍历性提供了几乎必要和充分的条件。此外，这些结果说明了作为参数对遍历性和灭绝条件的影响$\阿尔法$趋于2。