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Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality

机译：在长期平均标准下可持续收集政策：近优先态度

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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.
机译：本文在捕食者 - 猎物系统中开发了捕食者的最佳可持续收获策略。目标函数在路径明显的情况下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制剂只是一种理想化，本文假设环境受到具有快速跳闸速率的跳跃过程的扰动。在广泛的条件下，示出了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，构建了原始系统的控制策略。这样的方法使我们能够开发可持续的收获政策，导致近在最佳状态。为了治疗潜在问题，主要困难之一是由于长期的平均目标函数。这反过来又需要处理与ergodicity相关的许多问题。开发了新方法以获得基于人口动态系统的底层过程的紧张性。

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