An impulsive fishery model with environmental stochasticity. Feasibility

An environmental random-effect over a deterministic population model of a resource (e.g., a fish stock) is introduced. It is assumed that the harvest activity is concentrated at a non-predetermined sequence of instants, at which the abundance reaches a certain predetermined level, then falls abruptly by a constant capture quota (pulse harvesting). So, the abundance is modeled by a stochastic impulsive type differential equation, incorporating a standard Brownian motion in the per capita rate of growth. With this random effect, the pulse times are “stopping times” of the stochastic process. The proof of the finite expectation of the next access time, i.e., the feasibility of regulation, is the main result.