Numerical inversion of Laplace transform on the real line of probability density functions

A method for the numerical inversion of Laplace transform on the real line of a heavy-tailed probability density function is presented. The method ass umes as known a finite set of values of the Laplace transform and chooses t he analytical form of the approximant maximizing Shannon-entropy, so that p ositivity of the approximant itself is guaranteed. The problem resorts to a finite generalized moment problem and a stability analysis is also provide d. Some numerical results are illustrated. (C) 2001 Elsevier Science Inc. A ll rights reserved.