After reading the reference given by Denis,A Markov chain has transition matrix
\(\displaystyle \begin{pmatrix}1/3 & 0 & 2/3 & 0 & 0 \\
0 & 1/2 & 0 & 1/2 & 0 \\
3/4 & 0 & 1/4 & 0 & 0 \\
0 & 3/4 & 0 & 1/4 & 0 \\
1/3 & 0 & 1/3 & 0 & 1/3 \end{pmatrix}\)
Analyze the state space (reducibility, periodicity, recurrence, etc), and discuss the
chain's long run behavior.
I notice that your matrix does NOT have columns that sum to 1, so that sum of elements in the state vector is not conserved. Is it possible you have entered the Transpose of the transition matirx? What definitions are you using?Denis said:
\(\displaystyle \text{A Markov chain has transition matrix: }\;A \;=\;\begin{bmatrix}\frac{1}{3}&0&\frac{2}{3} &0&0 \\ 0&\frac{1}{2}&0&\frac{1}{2}&0 \\ \frac{3}{4}&0&\frac{1}{4}&0&0 \\ 0&\frac{3}{4} &0&\frac{1}{4}&0 \\ \frac{1}{3}&0&\frac{1}{3}&0& \frac{1}{3} \end{bmatrix}\)
\(\displaystyle \text{Discuss the chain's long run behavior.}\)