Rates of uniform convergence in the real inversion theorem for Laplace transforms
Jose Antonio Adell, C. Sangüesa · Mathematical Proceedings of the Cambridge Philosophical Society · 1999
We obtain sharp rates of uniform convergence in the real inversion theorem for Laplace transforms. This entails giving estimates of the Kolmogorov distance between normalized Poisson mixtures and their mixing distribution. Our approach combines probabilistic representations in terms of gamma processes with approximation-theoretic techniques.