A Two-State, Discrete-Time Markov Chain

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Consider a system that is always in one of two states, 1 or 2. Every time a clock ticks, the system updates itself according to a 2×2 matrix of transition probabilities, the entry of which gives the probability that the system moves from state
to state
at any clock tick. A twoâÃÂÃÂstate Markov chain is a system like this, in which the next state depends only on the current state and not on previous states. Powers of the transition matrix approach a matrix with constant columns as the power increases. The number to which entries in the
column converge is the asymptotic fraction of time the system spends in state
.
Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA
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"A Two-State, Discrete-Time Markov Chain"
http://demonstrations.wolfram.com/ATwoStateDiscreteTimeMarkovChain/
Wolfram Demonstrations Project
Published: March 7 2011