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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

N ˙(t)=(r+αB ˙(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:
34F05ODE with randomness
60H10Stochastic ordinary differential equations
34A55Inverse problems of ODE
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