Let p_ij(t) be the probability that a stochastic process takes on value j at “time” t (discrete or continuous), given that it began at time 0 from state i. If p_ij(t) approaches a limit p_j independent of i at t →∞ for all j, we say that the process is in statistical equilibrium. If a Markov chain has a limiting distribution, then this distribution is identical to the stationary one found by solving π = πP.v  Limiting distribution;  Markov chains;  Markov processes; Stationary distribution; Steady-state distribution.