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Application of Matrix Rank in Judging the Ergodicity of Homogeneous Markov Chains

ZHAO Wei-hua,SHU Jian(Nantong University,Nantong 226019,China)  
Applying general methods sometimes makes it difficult to judge the ergodicity of homogeneous Markov chains.As a new way of judgment,the matrix rank is introduced.Assume {Xk,k≥0} is a homogeneous Markov chain with n states,R(Z) = m,then when m = n,{Xk,k≥0}has its ergodicity;when m n,ergodicity doesn′t exist in {Xk,k≥0}.It is simpler and more convenient for us to use the conclusion to judge ergodicity of homogeneous Markov chains.The effectiveness and accuracy of the method are obviously shown by two examples.
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