Transcription of 1 Limiting distribution for a Markov chain
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1 Limiting distribution for a Markov chain
Copyrightc 2009 by Karl Sigman1 Limiting distribution for a Markov chainIn these Lecture Notes, we shall study the Limiting behavior of Markov chains as timen .In particular, under suitable easy-to-check conditions, we will see that a Markov chain possessesa Limiting probability distribution , = ( j)j S, and that the chain , if started off initially withsuch a distribution will be a stationary stochastic process. We will also see that we can find by merely solving a set of linear Communication classes and irreducibility for Markov chainsFor a Markov chain with state spaceS, consider a pair of states (i,j).
1. 2.3 Limiting stationary distribution ˇ 0 ˇ = i); is called the limiting or stationary or steady-state distribution of the Markov chain.
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