Past exam of the probability course of the University of Oxford / 2017 / 3 / a / ii / Solution

A stationary distribution is a nonnegative row vector $\pi =({\pi }_i{)}_{i\in S}$ with total mass one that is preserved by one transition:In matrix notation, $\pi P=\pi$. If the initial state has distribution $\pi$, so does the state at each later time.