A Complete Coupling Proof of Blackwell's Renewal Theorem.
Abstract
Blackwell's renewal theorem for non-lattice renewal processes with mean recurrence time m states that the expected number of renewals in a time-interval of length h tends to h/m as the interval goes to infinity: E(N(t,t + h)) approaches h/m as t approaches infinity. This note presents a self contained coupling proof of this result mending the drawbacks of earlier such proofs. Firstly, the proof is complete in the sense that it covers not only the case m < infinity but also m = infinity. Secondly, the proof is fairly elementary in the sense that it does not rely on advanced results such as Hewitt-Savage 0-1-Law or the epsilon-recurrence of 0-mean random walks.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1987
- Accession Number
- ADA176840
Entities
People
- Hermann Thorisson
Organizations
- Stanford University