# hitting time

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

^{}:

$${H}^{A}=inf\{n\ge 0:{X}_{n}\in A\}$$ |

(set $inf\mathrm{\varnothing}=\mathrm{\infty}$).

This can be thought of as the time before the chain is first in a state that is a member of $A$.

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

$$ |

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

Title | hitting time |
---|---|

Canonical name | HittingTime |

Date of creation | 2013-03-22 14:18:18 |

Last modified on | 2013-03-22 14:18:18 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 8 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 60J10 |

Related topic | MarkovChain |

Related topic | MeanHittingTime |

Defines | absorption probability |