Appl Math Optim https://doi.org/10.1007/s00245-018-9504-y Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality 1 2 Dang H. Nguyen · George Yin © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract 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 ide- alization, 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 har- vesting 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
Applied Mathematics and Optimization – Springer Journals
Published: May 28, 2018
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