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Unique stationary distribution

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asked Apr 25, 2018 in BUS 3018F - Models by anonymous

What is a unique stationary probability distribution? Why does an irreducible markov chain with finite state space have this unique stationary distribution? 

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answered Apr 25, 2018 by TinoM (140 points)

A stationary probability distribution in the context of markov chains is a probability distribution which does not change as the process progresses. An irreducible finite markov chain is a chain in which the process can reach any state regardless where it starts (It has no absorbing states). Given the state space is finite it means the probability of transitioning from one state to another which is irrespective of time (and past movements since it is markov) has to be unique.