Exponential Stability Of A Class Of Nonlinear Stochastic Differential Equations

In recent years, the stability of the stochastic system has been attracting more and more attention of the probability theory scholars and engineers and technical personnel-s, and has produced a lot of research results.Generally speaking, most of the predeces-sors’results start from the generator of the system and take Lyapunov method as the main tool,thus obtaining the stability criterion of the system.In this paper, starting from the transformation of stochastic differential equations, stochastic differential equations are partially transformed into ordinary differential equations with random items.Afterwards, through analyzing skills similar to the Hurwitz, the exponential stability condition of the system is obtained.Due to the fact that our condition needs only the derivative of the stochastic system in the equilibrium, our condition is more practical.