## ASYMPTOTIC EXPECTED NUMBER OF PASSAGES OF A RANDOM WALK THROUGH AN INTERVAL

Autor(en): | Kella, Offer Stadje, Wolfgang |

Stichwörter: | generalized renewal theorem; Mathematics; passage; Random walk; Statistics & Probability; two-sided renewal theorem |

Erscheinungsdatum: | 2013 |

Herausgeber: | CAMBRIDGE UNIV PRESS |

Journal: | JOURNAL OF APPLIED PROBABILITY |

Volumen: | 50 |

Ausgabe: | 1 |

Startseite: | 288 |

Seitenende: | 294 |

Zusammenfassung: | In this note we find a new result concerning the asymptotic expected number of passages of a finite or infinite interval (x, x h] as x -> infinity for a random walk with increments having a positive expected value. If the increments are distributed like X then the limit for 0 < h < infinity turns out to have the form E min(vertical bar X vertical bar, h)/EX, which unexpectedly is independent of h for the special case where vertical bar X vertical bar <= b < infinity almost surely and h > b. When h = infinity, the limit is E max(X, 0)/EX. For the case of a simple random walk, a more pedestrian derivation of the limit is given. |

ISSN: | 00219002 |

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