Numerical Bounds on Fluctuating Linear Processes

Let A be an n n primitive nonnegative matrix. The long-run behavior xk xk 1 of the linear process xk 1 xkA is determined by the stochastic eigenvector of A. In this paper we consider the linear process xk 1 xkAk, where each Ak fluctuates about A, and provide numerical bounds on the difference between xk xk and , thus showing how well describes the long-run behavior of this fluctuating behavior