论文标题
无限年龄结构粒子系统的动力学
Dynamics of an infinite age-structured particle system
论文作者
论文摘要
马尔可夫进化研究了无限年龄结构的移民人口，这些移民人口到达并从连续的栖息地$ x \ subseteq \ subseteq \ mathds {r}^d $ - 随机而彼此独立。每个人口成员的特征是其年龄$ a \ geq 0 $（人口的存在时间）和x $中的位置$ x \。人口状态是相应标记配置空间上的概率度量。本文的结果是通过为该模型求解标准的fokker-planck方程来构建此类状态的进化$μ_0\至μ_t$。如果移民率与零分开，我们还发现存在固定状态$μ$。然后显示出$μ_t$弱收敛到$μ$，为$ t \ to +\ infty $。
The Markov evolution is studied of an infinite age-structured population of migrants arriving in and departing from a continuous habitat $X \subseteq\mathds{R}^d$ -- at random and independently of each other. Each population member is characterized by its age $a\geq 0$ (time of presence in the population) and location $x\in X$. The population states are probability measures on the space of the corresponding marked configurations. The result of the paper is constructing the evolution $μ_0 \to μ_t$ of such states by solving a standard Fokker-Planck equation for this models. We also found a stationary state $μ$ existing if the emigration rate is separated away from zero. It is then shown that $μ_t$ weakly converges to $μ$ as $t\to +\infty$.
