IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains
A Markov chain on {1,2,3} has P(1,·)=(0.6,0.4,0), P(2,·)=(0,0.5,0.5), P(3,·)=(0,0,1). Which classification is correct?
States 1 and 2 are transient and state 3 is absorbing. Once the chain reaches state 3 it never leaves, so states 1 and 2 have a positive probability of never returning.
- AAll states are recurrent
- BStates 1 and 2 are transient and state 3 is absorbingCorrect
- CState 1 is absorbing and state 3 is transient
- DState 2 is recurrent because it has a self-transition
- The chain is irreducible
Explanation
State 3 has P(3,3)=1, so it is absorbing and recurrent. From 1 the chain can reach 2 and then 3, but never returns from 3, so 1 and 2 are transient. A self-loop does not make state 2 recurrent.
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