Almost sure permanence of stochastic single species models

A new definition of almost sure permanence of stochastic population systems is proposed in this paper. We consider the stochastic logistic modeldx(t)=x(t)[a(t)−b(t)xθ(t)]dt+σ(t)x(t)dB(t), where B(t) is a standard Brownian motion and θ is a positive constant. Under a simple assumption, a interesting result is obtained as follows:0