beamer - Vrije Universiteit Amsterdam

Full Case
.
Ergodic Theorem 3.3.3 and 3.5.11
.
Assume
.
(i). Unichain with finite transient set;
(ii). ∑
j∈I |f (j)|πj < ∞.
Then
Proof: see book.
1
lim
n→∞ n
n∑
f (Xk) = ∑
πjf (j) (w.p. 1)
k=1
j∈I
c⃝ Ad Ridder (VU) SOR– Fall 2012 30 / 36