Absorbing State

A Absorbing State is a state that impossible to leave.

• Context:
  • A state [math]\displaystyle{ s_i }[/math] of a Markov chain is called absorbing if it is impossible to leave it. A state which is not absorbing is called transient.
  • …
• Counter-Example(s):
  • Transient State

See: Markov Process State, Graph Path, Markov Chain, Accessible State, Recurrent State, Transient State, Absorbing Barrier.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Markov_chain#Abdosrbing_States
  • A state i is called absorbing if it is impossible to leave this state. Therefore, the state i is absorbing if and only if

[math]\displaystyle{ p_{ii} = 1\text{ and }p_{ij} = 0\text{ for }i \not= j. }[/math]

If every state can reach an absorbing state, then the Markov chain is an absorbing Markov chain.

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