The Application Of Split Chain

In this paper we introduce split chain and analyze the connecting the split and original chains.The splitting construction is valueble because of the various proper-ties that Φ inherits from Φ.Then we deduce the convergence of total variation norm on the discrete state space.The improtant thing is that we introduce the first-entrance last-exit decom-positions and regenerative decomposition. In order to use the splitting technique for analysis of total variation norm convergence for general state space chains we must extend the first-entrance last-exit decomposition to general spaces.Finally, we research convergence of total variation norm if there exists an ergodic atom.