Numerical inversion of the Laplace transform via fractional moments

摘要

A method for the numerical inversion of Laplace transform on the real line of heavy-tailed (probability) density functions is presented. The method assumes as known a finite set of real values of the Laplace transform and chooses the analytical form of the approximant maximizing Shannon-entropy, so that positivity of the approximant itself is guaranteed. The problem resorts to a finite fractional Hausdorff moment problem and some results of convergence are provided. Some numerical results are illustrated.