Uniform Renewal Theory with Applications to Expansions of Geometric Sums (with P. Glynn).

Summary:

This paper studies rates of convergence in the key renewal theorem uniformly over a class of distributions whose moments are uniformly controlled and that have a common component that is absolutely continuous with respect to the Lebesgue measure (actually the condition is slightly weaker). There are related results by Fuh and Borovkov and Foss (see cited references). A nice thing is that we also allow the drift of the inter-arrival distributions approach zero. We need also this asymptotic regime for the analysis of Geometric sums with mean zero increments.

Bibtex:

@Article{BlaGlyRT07,

author = { J. Blanchet and P. Glynn},

title = {Uniform renewal theory with applications to expansions of geometric sums},

journal = {Advances in Applied Probability},

year = {2007},

volume = {4},

pages = {1070-1097}

}