The authors in their papers (Liao and Mao, Stochast. Anal. Appl. 14 (2) (1996a) 165-185; Neural, Parallel Sci. Comput. 4 (2) (1996b) 205-244) initiated the study of stability and instability of stochastic neural networks and this paper is the continuation of their research in this area. The main aim of this paper is to discuss almost sure exponential stability for a stochastic delay neural network dx(t) = [-Bx(t) + Ag(xτ(t))]dt + σ(x(t),g(xτ(t),t)dw(t). The techniques used in this paper are different from those in their earlier papers. Especially, the nonnegative semimartingale convergence theorem will play an important role in this paper. Several examples are also given for illustration.
- Brownian motion
- delay neural network
- exponential stability
- Lyapunov exponent
- Martingale convergence theorem