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CONDITIONS FOR STRONG ERGODICITY

Using Intensity Matrices, Jean Thomas Johnson, Dean Isaacson

Abstract

Sufficient conditions for strong ergodicity of discrete-time non-homogeneous Markov chains have been given in several papers. Conditions have been given using the left eigenvectors W, of P,,(nP, = Vn) and also using the limiting behavior of P,. In this paper we consider the analogous results in the case of continuous-time Markov chains where one uses the intensity matrices Q(t) instead of P(s, t). A bound on the rate of convergence of certain strongly ergodic chains is also given.

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Key concepts: Ergodicity, Markov chain, Mathematics, Ergodic theory, Stationary ergodic process, Eigenvalues and eigenvectors, Upper and lower bounds, Convergence (economics)