Category:Definitions/Absorbing States

This category contains definitions related to Absorbing States.
Related results can be found in Category:Absorbing States.

Let $\sequence {X_n}_{n \mathop \ge 0}$ be a Markov chain on a state space $S$.

Let $i \in S$ be an element of the state space $S$.

Then $i$ is an absorbing state of $\sequence {X_n}$ if and only if:

$X_k = i \implies X_{k + 1} = i$

That is, it is an element of $S$ such that if $\sequence {X_n}$ reaches $i$, it stays there.