Abstract
In this paper, we further consider the problem of stochastic finite-time stability and instability of nonlinear stochastic differential equations (SDEs) with time-varying drift and diffusion terms. The contributions of the paper are highlighted as follows. Some new conditions via multiple Lyapunov functions are given for stochastic finite-time stability of nonlinear time-varying SDEs. Compared with the existing results on stochastic finite-time stability, the constraint of the differential operator is further relaxed in this paper, which enable us to construct the Lyapunov functions much more easily in applications for nonlinear time-varying SDEs. In addition, a stochastic finite-time instability theorem is proposed, and it shows the necessity of in the proposed conditions of stochastic finite-time stability. Some examples are presented to illustrate the new results.
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