Application of Matrix Rank in Judging the Ergodicity of Homogeneous Markov Chains
Shu Jian · Journal of Nantong University · 2009
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.