Solution
= Solution
A distribution $\pi$ is an <invariant distribution> when
$$
\pi_j=\sum_{i\in S}\pi_i p_{ij}
$$
for every $j$, equivalently $\pi P=\pi$.
= Solution
A distribution $\pi$ is an <invariant distribution> when
$$
\pi_j=\sum_{i\in S}\pi_i p_{ij}
$$
for every $j$, equivalently $\pi P=\pi$.