Coefficients of ergodicity with respect to vector norms

Abstract

The stationary distribution may be used to estimate the rate of geometric convergence to ergodicity for a finite homogeneous ergodic Markov chain. This is done by invoking the spectrum localization property of a new class of ergodicity coefficients defined with respect to column vector norms for the transition matrix P. Explicit functional forms in terms of the entries of P are obtained for these coefficients with respect to the l∞ and l1, norms, and comparison in performance with various known coefficients is made with the aid of numerical examples.