I am solving a paper, in which there is a very large Markov chain. How can I find the steady state probability of a very large Markov chain since solving it through eigenvector process is proving to very difficult. I have attached the Markov chain in the link below
Markov Chain with large set of states
The authors claim that the steady state is following:
The Steady-State Probabilities as stated by authors
$$\pi_{i,j}= \begin{cases} \pi_{-1,-1} \cdot q, & \text{for }i=0 \text{ and } j=0 \\ \pi_{-1,-1} \cdot q \cdot p^i, & \text{for }i \in [1,M] \text{ and } j=0 \\ \pi_{-1,-1} \cdot q \cdot \frac{W-j}{W}, & \text{for }i \in [1,M] \text{ and } j \in [0, W-1] \\ \end{cases}$$