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Stochastic models as functionals: some remarks on the renewal case

Published online by Cambridge University Press:  14 July 2016

Rudolf Grübel
Rudolf Grübel*
Affiliation:
Imperial College, London
*
∗ Postal address: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.
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Abstract

We regard the standard stochastic model of renewal theory as a functional which associates with a lifetime distribution μ the corresponding renewal measure v = Σ0 ∞μ ∗n . The behaviour of this functional near exponential distributions is investigated. The literature mainly deals with the asymptotic behaviour of v([0, t]) and v[t, t + 1]) as t → ∞— this new approach leads to expansions which are valid uniformly in t ∈ R.

Keywords

RENEWAL THEORYLIFETIME DISTRIBUTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989, pp. 296 - 303
Copyright
Copyright © Applied Probability Trust 1989 

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References

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