论文标题
基于观察的人口动态管理模型及其生态应用
A random observation-based management model of population dynamics and its ecological application
论文作者
论文摘要
在数学和数值上，对部分观察的种群动态的新随机控制问题进行了制定和分析，并着重于环境和生态问题。决策者只能随机且谨慎地观察和冲动干预受政权转换随机微分方程控制的人群动态。问题的混合性质导致一个最优方程，其中包含一个差异方程和静态优化问题。因此，它与常规的汉密尔顿 - 雅各比 - 贝尔曼方程式不同。该最优方程的存在和可溶性问题以粘度意义进行分析。它对还原但仍然非平凡模型的确切解决方案也得出了。该模型最终使用有限的差异方案应用于河流中现实的环境管理问题。
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only randomly and time-discretely observe and impulsively intervene the population dynamics governed by a regime-switching stochastic differential equation. The hybrid nature of the problem leads to an optimality equation containing an integro-differential equation and a static optimization problem. It is therefore different from the conventional Hamilton-Jacobi-Bellman equations. Existence and solvability issues of this optimality equation are analyzed in a viscosity sense. Its exact solution to a reduced but still nontrivial model is derived as well. The model is finally applied to a realistic environmental management problem in a river using a finite difference scheme.
