According to the Lifshitz-Slezov theory of Ostwald ripening and its generalizations in the asymptotic stage of the competitive growth of an ensemble of clusters, a time-independent cluster size distribution in reduced coordinates is established. The shape of this distribution deviates, however, from the experimentally observed curves, which are in general broader and more symmetric, A number of different proposals have been developed in the literature for an explanation of this discrepancy. Here it is shown that the influence of stochastic effects on coarsening due to thermal noise, which has not been considered so far, may significantly diminish the gap between experiment and theory.