Operator-Theoretical Treatment of Ergodic Theorem and Its Application to Dynamic Models in Economics

The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains that are frequently used in dynamic economic models to be ergodic. The paper reviews the time average convergence of the quasi-weakly complete continuity Markov operators to a unique projection operator. Also, it shows that a further assumption of quasi-strongly...