Is an absorbing state considered transient or recurrent?

Is an absorbing state considered transient or recurrent?

• A. Transient
• B. Recurrent
• C. Neither
• D. Periodic

Answer: (B)

An absorbing state is one you cannot leave once entered. In a Markov chain, that means if you start in that state, you stay there forever, so you will be in that same state at all future times. This makes the probability of ever returning to the state (starting from it) equal to 1, which is exactly the definition of a recurrent state. It isn’t transient, because transient states are those you are certain to leave and never return to. (If you want a quick note, absorbing states are aperiodic, since you can remain in the state at every step, giving period 1, but the question focuses on recurrent versus transient.)

An absorbing state is one you cannot leave once entered. In a Markov chain, that means if you start in that state, you stay there forever, so you will be in that same state at all future times. This makes the probability of ever returning to the state (starting from it) equal to 1, which is exactly the definition of a recurrent state. It isn’t transient, because transient states are those you are certain to leave and never return to. (If you want a quick note, absorbing states are aperiodic, since you can remain in the state at every step, giving period 1, but the question focuses on recurrent versus transient.)