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# hitting time

Let $(X_{n})_{{n\geq 0}}$ be a Markov Chain. Then the *hitting time* for a subset $A$ of $I$ (the indexing set) is the random variable:

$H^{A}=\inf\{n\geq 0:X_{n}\in A\}$ |

(set $\inf\varnothing=\infty$).

Wite $h_{i}^{A}$ for the probability that, starting from $i\in I$ the chain ever hits the set A:

$h_{i}^{A}=P(H^{A}<\infty:X_{0}=i)$ |

When A is a closed class, $h_{i}^{A}$ is the *absorption probability*.

Defines:

absorption probability

Related:

MarkovChain, MeanHittingTime

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

60J10*no label found*

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