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March 16th, 2009, 04:41 PM  #1 
Newbie Joined: Nov 2007 Posts: 3 Thanks: 0  Markov chain and classifying states
Given the transition matrices below, find all communicating classes and classify all states: The probabilities don't matter for this exercise, so I'm just going to put ones for nonzero entries, even though I know this is absurd mathematically: (A) 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 I believe that the communicating classes are {1,2,4} and {3} and all these are ergodic. (B) 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 I think the communicating classes are {1,3}, {2}, and {4}. I'm not quite sure, but I believe states 1,3, and 4 are ergodic, and 3 is of period 2. (C) 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 The communicating classes are {1,2} and {3,4} with {1,2} of period 2 and {3,4} ergodic. Is this right? I think I have the communicating classes right, but I'm not sure about the state classifications. Thanks in advance for any help. 

Tags 
chain, classifying, markov, states 
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