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 assumes as known a finite set of 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 generalized moment problem and a stability analysis is also provided. Some numerical results are illustrated.