For a time-homogeneous discrete time Markov chain, a reversible distribution of the chain is defined as $\pi$ that satisfies: $ π_i p_{ij} = π_j p_{ji}, \forall i, j. $
I was wondering if a reversible distribution is unique when exists?
Thanks!
For a time-homogeneous discrete time Markov chain, a reversible distribution of the chain is defined as $\pi$ that satisfies: $ π_i p_{ij} = π_j p_{ji}, \forall i, j. $
I was wondering if a reversible distribution is unique when exists?
Thanks!
Thanks to did! When the states are all isolated, $p_{ij}$ are all zero for $i \neq j$, so any distribution can be reversible.