Numerical bounds on fluctuating linear processes (Q5927713)

Let \(A\) be an \(n\times n\) primitive nonnegative matrix. The long-run behavior \(x_k/\|x_k\|_1\) of the linear process \(x_{k+1}=x_k A\) is determined by the stochastic eigenvector \(\pi\) of \(A\). The author considers the linear process \(x_{k+1}=x_k A_k\), where each \(A_k\) fluctuates about \(A\), and provides numerical bounds on the difference between \(x_k/\|x_k\|\) and \(\pi\), thus showing how well \(\pi\) describes the long-run behavior of this fluctuation behavior.