Stationarity equations
= Stationarity equations
{title2=$\pi_j=\sum_i\pi_iP_{ij}$}
For a discrete-time <Markov chain> with <transition matrix> $P$, these equations, together with $\pi_j\geq0$ and $\sum_j\pi_j=1$, say that $\pi$ is a <stationary distribution>. Incoming <probability> mass equals the current mass at each state. They are global balance equations and do not require <detailed balance>.