Approximation of probabilistic Laplace transforms and their inverses

Abstract

We present a method to approximate the law of positive random variables defined by their Laplace transforms. It is based on the study of the error in the Laplace domain and allows for many behaviors of the law, both at $0$ and infinity. In most cases, both the Kantorovich/Wasserstein error and the Kolmogorov–Smirnov error can be accurately computed. Two detailed examples illustrate our results.