A study of stochastic iterative processes under random structural perturbations

Stochastic processes have enjoyed a wide variety of applications from engineering to learning theory to economics. In this work, systems of iterative stochastic processes with random structural perturbations are studied. Sufficient conditions for the stability and convergence of these processes are developed using comparison theorems in the context of both scalar and vector Lyapunov functions. The effects of the structural perturbations on the stability of the iterative stochastic processes are presented. In addition, a comparison is made between the effects of the scalar Lyapunov function verses the vector Lyapunov function. The usefulness and scope of the theory presented are demonstrated in the convergence and stability of an application from the field of economics.