Cesaro limits of analytically perturbed stochastic matrices
Let \(P_0\) be a stochastic matrix with no eigenvalue other than \(1\) on the unit circle and let \(P(\varepsilon)=P_0+A(\varepsilon)\) be an analytic perturbation which is still stochastic for small enough positive \(\varepsilon\). The authors determine the limit \(\lim_{\varepsilon\downarrow 0}\frac 1{N(\varepsilon)}\sum_{l=1}^{N(\varepsilon)} P^l(\varepsilon)\), where \(N(\varepsilon)\uparrow\infty\) at various rates.
scientific article; zbMATH DE number 1800361