Steady-state distribution

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, the set pv = {p _j} is called the limiting or steady-state distribution of the process. For Markov chains in discrete time, the existence of a limiting distribution implies that there is a stationary distribution found from π = πPv and that π = p.v For continuous-time chains, the steady-state distribution is the probability vector satisfying the global balance equations πQv = 0. Limiting distribution; Markov chains; Markov processes; Stationary distribution; Statistical equilibrium.