Solution
= Solution
The stationary equation $\pi Q=0$ reads $r^T-R\pi=0$, because $\pi\mathbf1=1$. Therefore
$$
\boxed{\pi_j=\frac{r_j}{R}.}
$$
It is the unique stationary law and vanishes on the open classes. For distinct $i,j$, $\pi_iq_{ij}=r_ir_j/R=\pi_jq_{ji}$. Thus \b[the chain is reversible in its equilibrium law], including the reducible cases; on the closed class this is the usual reversible irreducible chain. This structure is the <destination-dependent reset chain>.