  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 complete continuity reduces
the dependence of the unique invariant measure on its corresponding initial
distribution through ergodic decomposition, and therefore guarantees the Markov
chain to be ergodic up to multiplication of constant coefficients. Moreover, a
sufficient and practical condition is provided for the ergodicity in economic
state Markov chains that are induced by exogenous random shocks and a
correspondence between the exogenous space and the state space.
