Absorbing Set

Topics: State Set - Stochastic Process

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(definition)

An ergodic set with a single element is called an absorbing set. This single element of an absorbent set is called an absorbing state.

It is called so because once we reach such a state, it absorbs the process and it will remain there forever.

A Markov chain whose every non-transitory state is absorbing is also said to be absorbing.

(observation)

Note that a state $k$ is absorbing if $p_{kk}=1$.