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Renewal excess limit theorem

For non-arithmetic inter-renewal times with finite positive mean

μ

, the excess

E (t) = S_{N (t) + 1} - t

converges in distribution to

E_{\infty}

with

P (E_{\infty} > x) = \frac{1}{μ} \int_{x}^{\infty} P (ξ_{1} > y) d y .

Table of contents 76 1
- Exponential first interarrival in a renewal superposition containing a Poisson process Renewal excess limit theorem 53

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