Limit Theorem for markov chains n=base at generationn Pi=P(Sn+1=jiN=i) Pij >0 for all i,j(and ∑P=1fora0 then there is a unique vector r such that r=rp and ling pn=r for any prob. vector q n→>00 r is called the"stationary"or"limiting" distribution of P See Ch 4, Taylor Karlin, An Introduction to Stochastic Modeling, 1984 for detailsLimit Theorem for Markov Chains Sn = base at generation n Pij = P ( Sn +1 = j |Sn =i ) If Pij >0 for all i,j (and ∑ Pij =1 for all i) j G then there is a unique vector P n G r P G r r such that G q G r G = and lim = (for any prob. vector q ) n → ∞ G r is called the “stationary” or “limiting” distribution of P See Ch. 4, Taylor & Karlin, An Introduction to Stochastic Modeling, 1984 for details