beamer - Vrije Universiteit Amsterdam

Summary
Suppose Assumption 3.3.1 (equivalently, unichain with finite transient set T
and positive recurrent set R). Suppose aperiodicity of the recurrent states.
Then
1. There is a unique equilibrium distribution π = (πj)j∈I:
2. πj = 0 for j ∈ T and πj > 0 for j ∈ R;
3. π is the limiting distribution:
π = πP
lim
n→∞ p(n) ij = πj
4. π is the long-run average distribution:
1
lim
n→∞ n
n∑
k=1
p (k)
ij
= πj
c⃝ Ad Ridder (VU) SOR– Fall 2012 27 / 36