Difference equations of Ricker and logistic types under bounded stochastic perturbations with positive mean

Existence, uniqueness, stochastic persis

Existence, uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation

✍ Chunyan Ji; Daqing Jiang; Ningzhong Shi; Donal O'Regan 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 128 KB

## Abstract This paper discusses a randomized logistic equation equation image with initial value __x__(0)=__x__~0~>0, where __B__(__t__) is a standard one‐dimension Brownian motion, and θ∈(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any