beamer - Vrije Universiteit Amsterdam
beamer - Vrije Universiteit Amsterdam
beamer - Vrije Universiteit Amsterdam
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Probabilistic Averages IV<br />
.<br />
Corollary<br />
.<br />
Suppose that the Markov chain satisfies the unichain condition with a finite<br />
set of transient states (|T| < ∞). Then for all states i, j ∈ I<br />
1<br />
lim<br />
n→∞ n<br />
. (i.e., independent of the initial state).<br />
n∑<br />
k=1<br />
p (k)<br />
ij<br />
= πj<br />
Proof: πj = 0 for transient j; and fij = 1 for recurrent j (see slide 7). Then<br />
apply slide 15.<br />
c⃝ Ad Ridder (VU) SOR– Fall 2012 17 / 36
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