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.
"Convergence of Simar's Algorithm for Finding the Maximum Likelihood Estimate of a Compound Poisson Process." Ann. Statist. 10 (3) 1006 - 1008, September, 1982. https://doi.org/10.1214/aos/1176345890