Real Inversion Formulas for Laplace and Stieltjes Transforms

摘要

We provide probabilistic proofs for a number of real inversion formulas for the Laplace and for the Stieltjes transform. The main drawback of the method used in this paper is that the revelant integral transform has to be recovered from a potential inversion formula. The main virtue of the paper lies in singling out the relevance of the asymptotic behavior of the sequence d sub n for n to infinity; probabilistic arguments often provide this behavior immediately.