Qualitative properties of stochastic iterative processes under random structural perturbations

In this work, under different modes of stochastic convergence, several convergence and stability results for stochastic iterative processes are developed. Difference inequalities and a comparison method in the context of Lyapunov-like functions are utilized. The presented method does not demand the knowledge of the probability distributions of solution processes. By decomposing random perturbations in nonlinear iterative processes into internal and external random perturbations, effects of these stochastic disturbances on the convergence and the stability of the the iterative processes are investigated. In fact, it is shown that the convergence and stability analysis is robust under random structural perturbations. The presented conditions are easy to verify, algebraically simple, and computationally attractive. The results provide new tests for distributed iterative processes in decentralized external regulation, adaptation, parameter estimation and the numerical analysis schemes.