A Simple Stochastic Process Model for River Environmental Assessment Under Uncertainty
A Simple Stochastic Process Model for River Environmental Assessment Under Uncertainty
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DOI：
10.1007/978-3-030-50436-6_36
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发表时间：
2020-05-25
期刊：
影响因子：
--
通讯作者：
Yoshioka Y
中科院分区：
文献类型：
--
作者：
Yoshioka H;Tsujimura M;Hamagami K;Yoshioka Y
我们考虑了一个新的简单的随机单物种种群动力学模型来理解不确定河流环境中流量调节的底栖藻类繁殖：一个工程问题。种群动态受状态切换流条件的影响，因此种群在高流量状态下有效移除，而在低流量状态下根本不移除。本文的重点是在模型不确定性下对藻华的负效用进行鲁棒性和数学上严格的统计评估。我们证明，如果求解由动态规划原理导出的最优性方程，该最优性方程是一个可能具有不连续系数的非线性和非局部退化椭圆方程的耦合系统，则可以得到评价。我们证明了系统在连续黏度和渐近意义上是可解的。并通过实例证明了它的解可以用收敛的有限差分格式进行数值逼近。
We consider a new simple stochastic single-species population dynamics model for understanding the flow-regulated benthic algae bloom in uncertain river environment: an engineering problem. The population dynamics are subject to regime-switching flow conditions such that the population is effectively removed in a high-flow regime while it is not removed at all in a low-flow regime. A focus in this paper is robust and mathematically rigorous statistical evaluation of the disutility by the algae bloom under model uncertainty. We show that the evaluation is achieved if the optimality equation derived from a dynamic programming principle is solved, which is a coupled system of non-linear and non-local degenerate elliptic equations having a possibly discontinuous coefficient. We show that the system is solvable in continuous viscosity and asymptotic senses. We also show that its solutions can be approximated numerically by a convergent finite difference scheme with a demonstrative example.
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