Second-order asymptotics in level crossing for differences of renewal processes

Dirk Kroese, W.C.M. Kallenberg

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Abstract

We consider level crossing for the difference of independent renewal processes. Second-order expansions for the distribution function of the crossing time of level n are found, as n - oo. As a by-product several other results on the difference process are found. The expected minimum of the difference process appears to play an important role in the analysis. This makes this problem essentially harder than the level crossing for the sum process which was studied earlier.
Original languageEnglish
Pages (from-to)309-323
Number of pages15
JournalStochastic processes and their applications
Volume40
Issue number2
DOIs
Publication statusPublished - 1992

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