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Optimal harvesting of stochastically fluctuating populations. (English) Zbl 0940.92029
Optimal harvesting of populations which fluctuate stochastically over time is considered. The problem was studied under the regime of three constraints; viz under an unbounded harvesting rate, under a bounded catch-per unit of effort and under the regime of bounded harvesting quotas. Stochastic calculus is used as a tool to study the problem. The stationary distribution for the population is explicitly calculated. The authors show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution.

92D40 Ecology
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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