Numerical inversion of Laplace transform on the real line from expected values

摘要

A numerical method for inversion of Laplace transform F(s) of probability densities, given for real s⩾0 only, is proposed. Fractional calculus allows us to have expected values from F(s) or F′(s). Then the maximum entropy technique provides the analytical form of the approximant. Fractional moments are mainly investigated. Entropy and cross-entropy convergence are proved. Some numerical tests are illustrated.