This paper develops near-optimal sustainable harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense. To date, ecological systems under environmental noise are usually modeled as stochastic differential equations driven by a Brownian motion. Recognizing that the formulation using a Brownian motion is only an idealization, in this paper, it is assumed that the environment is subject to disturbances characterized by a jump process with rapid jump rates. Under broad conditions, it is shown that the systems under consideration can be approximated by a controlled diffusion system. Based on the limit diffusion system, control policies of the original systems are constructed. Such an approach enables us to develop sustainable harvesting policies leading to near optimality. To treat the underlying problems, one of the main difficulties is due to the long-run average objective function. This in turn, requires the handling of a number of issues related to ergodicity. New approaches are developed to obtain the tightness of the underlying processes based on the population dynamic systems.

中文翻译：

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长期平均标准下的可持续采伐政策：接近最优

本文为捕食者—被捕食者系统中的捕食者开发了近乎最佳的可持续收获策略。从路径的角度来看，目标函数是每单位时间类型的长期平均值。迄今为止，环境噪声下的生态系统通常被建模为由布朗运动驱动的随机微分方程。认识到使用布朗运动的公式化只是一个理想化，在本文中，假设环境受到以快速跳跃率的跳跃过程为特征的干扰。结果表明，在较宽的条件下，所考虑的系统可以通过受控扩散系统来近似。基于极限扩散系统，构造了原始系统的控制策略。这种方法使我们能够制定可持续的采伐政策，从而实现接近最优的目标。要解决潜在的问题，主要困难之一是由于长期的平均目标函数。反过来，这需要处理与遍历有关的许多问题。开发了新的方法来获得基于人口动态系统的基础流程的紧密性。