I have a random walk Markov chain that has states from $0$ to $N$. The conditions are that when the chain is at $0$, the chain will go to state $1$ with probability $1$. When the chain is at state $N$, it will go to state $N-1$ with probability $1$ as well. However, for everything between, for any other states $k$, the chain will go to $k+1$ with probability $p_k$ and go to $k-1$ with probability $q_k$. I am trying to find the limiting distribution $\pi$. I feel like there is a very easy way to do this due to the structure of the matrix but I keep running into significant calculations. Does anyone see a hint here? Thanks.
2026-04-18 23:31:07.1776555067
How to determine the limiting distribution of a Markov Chain which can only increment up or down a state at every stage?
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