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Existence, uniqueness, and global attractivity of positive solutions and MLE of the parameters to the logistic equation with random perturbation. (English) Zbl 1136.34324
Noting that population systems are often subject to environmental noise, the authors consider the random logistic equation \[ \dot{N}(t)=(r+\alpha\dot{B}(t))N(t)[1-(N(t)/K)], \] where \(N(0)\) is a random variable satisfying \(0<N(0)<K\) and \(B(t)\) is a 1-dimensional standard Brownian motion. The existence, uniqueness and global attractivity of positive solutions are investigated, and maximum likelihood estimators of the parameters are found.

MSC:
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34A55 Inverse problems involving ordinary differential equations
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