In the above matrix how do I calculate the probability that in the long run the system will be in 1 of the absorbing states?In particular say the probability of being in the 1st absorbing state in the long run?Is it 0.5?

  • $\begingroup$ Surely it depends on whether you starts in 1,2,3 or 4... $\endgroup$ – Lost1 Jul 3 '14 at 11:02

The probability the Markov chain ends up in one of the absorbing states is $1$.

Let $p_i$ be the probability of absorption in state 1 when starting in state $i$

Note $p_2=0$ $p_1=1$

$$p_3 = 0.2p_1+0.6p_3+0.2p_4$$


write down the equation for $p_4$, then solve.

Let $q_i$ be the probability absorption in state 2, note that $q_i+p_i=1$ (why?)


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