The Ergodicity Of Markov Chains On General Space

Markov chains is a discrete event stochastic process with the property of Markov in mathematics.In the process,in the case of given current knowledge or information,the past(that is,the current historical state)is irrelevant to the prediction of the future(the future future state).This nature of the Markov chains is called Markov property.With the development of modern science and technology,Markov chains has been ap-plied in various fields of our lives,and ergodicity is one of the important contents in the research of Markov chains.When Markov chains meeting the requirement of min-imize conditions,it can be divided.Here we introduce split chains,including splitting of space,measure and Markov chains,and analyzes the relationship with the original chains and splitting chains according to the definition of split chains.The m-skeleton satisfied the minimize conditions when there is a small set,then it can split the chain,which will reach regeneration decomposition of Markov chains with accessible atom,and ergodicity of positive recurrent and aperiodic irreducible chain.