Abstract
In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we prove that the stochastic system under consideration has a unique global solution. Additionally, we also investigate the exponential stability of the mean square.
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