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December 3rd, 2013, 12:37 AM   #1
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markov chains

A random walker walks among 3 points labelled a,b,c: Each minute, she takes a step, and
her movement dynamics are as follows:
 If (current position) equals (previous-minute position), then go to any one of the other two positions
with equal probability;
 If (current position) does not equal (previous-minute position), then continue to stay in current position
during the next minute.
Determine the state-space, such that the system evolution can be described by a Discrete Time Markov
Chain. Justify your answer. Draw the state transition diagram, with the states labeled and the edges labeled
with the transition probabilities. Is the Markov chain irreducible and aperiodic?

I have just learnt Markov chains . How shall I go about this?
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