Inverse Laplace transform for heavy-tailed distributions

摘要

Laplace transform inversion on the real line of heavy-tailed (probability) density functions is considered. The method assumes as known a finite set of fractional moments drawn from real values of the Laplace transform by fractional calculus. The approximant is obtained by maximum entropy technique and leads to a finite generalized Hausdorff moment problem. Directed divergence and L1-norm convergence are proved.