beamer - Vrije Universiteit Amsterdam

Equilibrium Distribution
.
Definition 3.3.2
.
A probability distribution (πj)j∈I is an equilibrium distribution for the Markov
chain if
πj =
.
∑
πipij (j ∈ I)
i∈I
.
Corollary
.
Let π be an equilibrium distribution for the Markov chain {Xn, n = 0, 1, . . .}
and suppose that the chain starts in equilibrium, then it remains in
equilibrium; i.e.,
.
(X0 = j) = πj ∀j ∈ I ⇒ (Xn = j) = πj ∀j ∈ I ∀n = 1, 2, . . .
c⃝ Ad Ridder (VU) SOR– Fall 2012 23 / 36