Stochastic Persistence.
Stochastic Persistence.
复制标题
随机持久性。
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Michel Benaim
中科院分区：
文献类型：
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作者：
Michel Benaim
设$（X_t）_{t \geq 0}$是度量空间$M上的连续时间马氏过程，$留下不变的闭子集$M_0 \子集M，$称为{\em绝灭集}。我们给出了确保“随机持久性”（第一部分）的一般条件：占领测度的极限点是$M_+ = M \setminus M_0;$或“灭绝”（第二部分）：$X_t \rightarrow M_0$ a.s.在持久性情形中，我们还讨论了保证$（X_t）$的占有测度（相应的分布）a.s收敛（相应的指数全变差收敛）到$M_+上的唯一概率的条件。这些结果扩展和推广了以前的结果，各种随机模型的人口动态，随机微分方程，随机微分方程，或纯跳过程。
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence" (Part I) : Limit points of the occupation measure are invariant probabilities over $M_+ = M \setminus M_0;$ or "Extinction" (Part II) : $X_t \rightarrow M_0$ a.s. In the persistence case we also discuss conditions ensuring the a.s convergence (respectively exponential convergence in total variation) of the occupation measure (respectively the distribution) of $(X_t)$ toward a unique probability on $M_+.$ These results extend and generalize previous results obtained for various stochastic models in population dynamics, given by stochastic differential equations, random differential equations, or pure jump processes.