Convergence of Simar's Algorithm for Finding the Maximum Likelihood Estimate of a Compound Poisson Process

Simar (1976) suggested an iteration procedure for finding the maximum likelihood estimate of a compound Poisson process, but he could not show convergence. Here the more general case of maximizing a concave functional on the set of all probability measures is treated. As a generalization of Simar's procedure, an algorithm is given for solving this problem, including assumptions to ensure convergence to an optimum. Finally, it is shown that Simar's functional fulfills these assumptions.