Coefficients of ergodicity with respect to vector norms
Choon-Peng Tan · Journal of Applied Probability · 1983
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 l 1 , norms, and comparison in performance with various known coefficients is made with the aid of numerical examples.