Suppose I have a markov chain with finite state space $0,\ldots, N$. At each state $1, \ldots, N-1$, we have that the probability of going up and down one state is of probability $\frac{1}{2}$. Now, at $0,N$ it gets absorbed, meaning we go back to the state with probability $1$. I am trying to determine how many stationary measures they might be. My guess is $2$, is this correct?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
No, there's a continuum of stationary measures, with weight $p$ at $0$ and $1-p$ at $N$.
