MATLAB: Simulate a markov chain including the absorbing state “death”

absorbing state

I am simulating a Markov chain process with the transition probability matrix:
P = [0.9044 0.0099 0 0 0.0857;…
0 0.7287 0.1057 0.0799 0.0857;…
0 0.0699 0.8183 0 0.1118; …
0 0.376 0 0.6199 0.0041; …
0 0 0 0 1]
where I have five states = single, marriage, divorce, widow and death
When I run the simulations, I always end up with state 5 (which is death).
Should I not include the abosrbing state?

Best Answer

You won't always eventually die? While there are ways for that to not happen eventually, usually they are the plot of some movie. And if you DO know some way to avoid that particular absorbing state, you might consider selling the formula. my guess is there would be a few buyers at any cost.
Seriously, all states eventually allow transition into the absorbing state with some non-zero probability, so the long time state of the system would have you always in the absoring state. This is just an expected behavior for such a process.
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