论文标题
化学稳定模型的准平台行为：Crump-Young模型
Quasi-stationary behavior for an hybrid model of chemostat: the Crump-Young model
论文作者
论文摘要
Crump-Young模型由两个完全耦合的随机过程组成，这些过程对化学稳定物中的底物和微生物动力学进行了建模。底物遵循一个普通的微分方程，其系数取决于微生物的数量。微生物是通过纯跳跃过程建模的，其跳跃速率取决于底物浓度。从微生物种群消失的意义上，它几乎灭绝了。在这项工作中，我们表明，在不膨胀的条件下，其分布将指数级的收敛于准平台分布。由于确定性部分，Crump-Young模型的动力学被高度退化。然后，证明是原始的，由技术尖锐的估计值和准平台收敛的新方法组成。
The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of microorganisms number. Microorganisms are modeled though a pure jump process whose the jump rates depend on the substrate concentration. It goes to extinction almost-surely in the sense that microorganism population vanishes. In this work, we show that, conditionally on the non-extinction, its distribution converges exponentially fast to a quasi-stationary distribution. Due to the deterministic part, the dynamics of the Crump-Young model is highly degenerated. The proof is then original and consists of technical sharp estimates and new approaches for the quasi-stationary convergence.
