A random observation-based management model of population dynamics and its ecological application
Abstract
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.
Cite
@article{arxiv.2004.04844,
title = {A random observation-based management model of population dynamics and its ecological application},
author = {Hidekazu Yoshioka and Yuta Yaegashi and Motoh Tsujimura},
journal= {arXiv preprint arXiv:2004.04844},
year = {2020}
}