Inverse two-sided Laplace transform for probability density functions
The author studies numerical inversion of the two-sided Laplace transform corresponding to a positive function, typically a probability density function. He consideres the problem where the data are the values of the first \(M\) derivatives of \(F(s)\) at the origin, related to the moments \(\mu_j\), \(j= 0,1,\dots, M\) of the function \(f(t)\) through the relation: \[ (-1)^j{d^jF(s)\over ds^j}\Biggl|_{s=0}= \mu_j,\quad j\geq 0,\quad \mu_0= 1. \] Then the problem of recovering \(f(t)\) is equivalent to the Hamburger moment problem. As the \(M\) moments do not give a unique probability density, so a widely used criterion is to choose the one which maximizes the entropy.
scientific article; zbMATH DE number 1326312