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A Simple Coupling of Renewal Processes

T. Lindvall
Advances in Applied Probability
Vol. 24, No. 4 (Dec., 1992), pp. 1010-1011
DOI: 10.2307/1427724
Stable URL: http://www.jstor.org/stable/1427724
Page Count: 2
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Abstract

We use a simple coupling to prove the classical result that the renewal function U of a zero-delayed renewal process satisfies U(t)-λ .t→ λ 2μ 2/2 as t→ ∞ if the life-length distribution is of non-lattice type and has finite first and second moments μ and μ 2 respectively; λ is the renewal intensity, and is equal to 1/μ .

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