Partial moment stability of stochastic differential equations with a general decay rate

In the first part of this paper, we discuss the problem of partial pth moment stability of stochastic differential equation with general decay rate when the origin is an equilibrium point. The results are obtained by using the method of Lyapunov and generalised integral inequalities. In the second part, we develop the problem of partial pth moment stability with general decay rate when the origin is not an equilibrium point. Some necessary numerical examples are also provided to show the effectiveness of the addressed method.