The difference of two renewal processes level crossing and the infimum

Dirk Kroese

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3 Citations (Scopus)

Abstract

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.
Original languageUndefined
Pages (from-to)221-243
Number of pages22
JournalCommunications in statistics : Stochastic models
Volume8
Issue number2
DOIs
Publication statusPublished - 1992

Keywords

  • IR-98528
  • METIS-140668

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