Coefficients of ergodicity for imprimitive matrices

Abstract

In this paper the classical notion of coefficient of ergodicity for regular stochastic matrices is extended to imprimitive stochastic matrices. This coefficient is then used to obtain results on imprimitive stochastic matrices similar to those for the regular case. In particular, a cyclic type of convergence result, with convergence rate determined by the coefficient of ergodicity, is given

Keywords:

• Coefficient of ergodicity
• imprimitive matrix
• stochastic matrix
• convergence result
• convergence rate