Memoirs of the American Mathematical Society 2009; 117 pp; softcover Volume: 197 ISBN10: 0821842595 ISBN13: 9780821842591 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/197/922
 The authors establish some asymptotic expansions for infinite weighted convolution of distributions having regularly varying tails. Applications to linear time series models, tail index estimation, compound sums, queueing theory, branching processes, infinitely divisible distributions and implicit transient renewal equations are given. A noteworthy feature of the approach taken in this paper is that through the introduction of objects, which the authors call the Laplace characters, a link is established between tail area expansions and algebra. By virtue of this representation approach, a unified method to establish expansions across a variety of problems is presented and, moreover, the method can be easily programmed so that a computer algebra package makes implementation of the method not only feasible but simple. Table of Contents  Introduction
 Main result
 Implementing the expansion
 Applications
 Preparing the proof
 Proof in the positive case
 Removing the sign restriction on the random variables
 Removing the sign restriction on the constants
 Removing the smoothness restriction
 Appendix. Maple code
 Bibliography
