In this paper, we establish the almost sure asymptotic stability and decay solutions of a scalar stochastic difference equation with a non-hyperbolic equilibrium at the origin which is perturbed by a random term with a fading state-independent intensity. Also we arrived the convergence speed because it determines the maximum rate of change of the input non –stationaries in the uncertained domain that was tracked by the stochastic network. © RJPT All right reserved.