Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications

摘要

We establish some asymptotic expansions for infinite weighted convolution of distri-butions having regularly varying tails. Applications to linear time series models, tailindex estimation, compound sums, queueing theory, branching processes, infinitelydivisible distributions and implicit transient renewal equations are given. A noteworthy feature of the approach taken in this paper is that through theintroduction of objects, which we call the Laplace characters, a link is establishedbetween tail area expansions and algebra. By virtue of this representation approach,a unified method to establish expansions across a variety of problems is presentedand, moreover, the method can be easily programmed so that a computer algebrapackage makes implementation of the method not only feasible but simple.