论文标题
在生物管理中产生的模棱两可之下有界噪声过程的广义随机控制问题
A generalized stochastic control problem of bounded noise process under ambiguity arising in biological management
论文作者
论文摘要
本文的目标和贡献是对歧义下有界种群动态的随机控制问题的数学和数值分析，这是一个重要但不是充分研究的问题，重点是最佳方程式作为非线性抛物性抛物性抛物性抛物性抛物性部分全部不分化方程（PIDE）。歧义是由于缺乏对动力学中连续和跳跃噪声的知识，其优化在派迪中以非线性和非局部术语的形式出现。假设连续价值函数具有强大的动态编程原理，我们从粘度和分布观点来表征其解决方案。还提出了针对千古案例的数值计算，以补充数学分析。
The objectives and contributions of this paper are mathematical and numerical analyses of a stochastic control problem of bounded population dynamics under ambiguity, an important but not well-studied problem, focusing on the optimality equation as a nonlinear degenerate parabolic partial integro-differential equation (PIDE). The ambiguity comes from lack of knowledge on the continuous and jump noises in the dynamics, and its optimization appears as nonlinear and nonlocal terms in the PIDE. Assuming a strong dynamic programming principle for continuous value functions, we characterize its solutions from both viscosity and distribution viewpoints. Numerical computation focusing on an ergodic case are presented as well to complement the mathematical analysis.
