### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 221-243 |

Number of pages | 22 |

Journal | Communications in statistics : Stochastic models |

Volume | 8 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1992 |

### Keywords

- IR-98528
- METIS-140668

### Cite this

}

*Communications in statistics : Stochastic models*, vol. 8, no. 2, pp. 221-243. https://doi.org/10.1080/15326349208807222

**The difference of two renewal processes level crossing and the infimum.** / Kroese, Dirk.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - The difference of two renewal processes level crossing and the infimum

AU - Kroese, Dirk

PY - 1992

Y1 - 1992

N2 - We consider the difference process N of two independent renewal (counting) processes. Second-order approximations to the distribution function of the level crossing time are given. Direct application of the second-order approximation is complicated by the occurrence of an (in general) unknown term E[Mtilde], which denotes the expected minimum of the stationary version of N. However, this number is obtained for a wide class of processes N, using matrix-geometric techniques. Numerical experiments have been carried out, in which the new approximations were compared to simulation, first-order and/or exact results. These results confirm that the second-order approximations are considerably better than the (known) first-order ones. We consider the difference process N of two independent renewal (counting) processes. Second-order approximations to the distribution function of the level crossing time are given. Direct application of the second-order approximation is complicated by the occurrence of an (in general) unknown term E[Mtilde], which denotes the expected minimum of the stationary version of N. However, this number is obtained for a wide class of processes N, using matrix-geometric techniques. Numerical experiments have been carried out, in which the new approximations were compared to simulation, first-order and/or exact results. These results confirm that the second-order approximations are considerably better than the (known) first-order ones.

AB - We consider the difference process N of two independent renewal (counting) processes. Second-order approximations to the distribution function of the level crossing time are given. Direct application of the second-order approximation is complicated by the occurrence of an (in general) unknown term E[Mtilde], which denotes the expected minimum of the stationary version of N. However, this number is obtained for a wide class of processes N, using matrix-geometric techniques. Numerical experiments have been carried out, in which the new approximations were compared to simulation, first-order and/or exact results. These results confirm that the second-order approximations are considerably better than the (known) first-order ones. We consider the difference process N of two independent renewal (counting) processes. Second-order approximations to the distribution function of the level crossing time are given. Direct application of the second-order approximation is complicated by the occurrence of an (in general) unknown term E[Mtilde], which denotes the expected minimum of the stationary version of N. However, this number is obtained for a wide class of processes N, using matrix-geometric techniques. Numerical experiments have been carried out, in which the new approximations were compared to simulation, first-order and/or exact results. These results confirm that the second-order approximations are considerably better than the (known) first-order ones.

KW - IR-98528

KW - METIS-140668

U2 - 10.1080/15326349208807222

DO - 10.1080/15326349208807222

M3 - Article

VL - 8

SP - 221

EP - 243

JO - Stochastic models

JF - Stochastic models

SN - 1532-6349

IS - 2

ER -