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
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.
