We study the uniform convergence to quasi-stationarity of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka–Volterra birth and death processes and Feller diffusions with competitive Lotka–Volterra interaction. To this aim, we develop an original non-linear Lyapunov criterion involving two functions, which applies to general Markov processes.

中文翻译：

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吸收马尔可夫过程的条件分布的均匀收敛的Lyapunov准则

我们研究了其中一个坐标消失时所吸收的多维过程的准平稳一致收敛。我们的结果涵盖了竞争性或弱合作性的Lotka-Volterra的出生和死亡过程以及具有竞争性Lotka-Volterra相互作用的Feller扩散。为此，我们开发了涉及两个函数的原始非线性Lyapunov准则，该准则适用于一般的Markov过程。