Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions

Abstract

We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results. © 2007 Springer-Verlag.