In an effort to provide probabilistic measures of the accuracy of population projections, stochastic models for population growth are defined from the classical discrete deterministic model by assuming respectively that (1) the deterministic model is subject to additive random errors; (2) the elements of the transition matrix represent probabilities, rather than rates; and (3) the transition matrices are random variables. The mean of each process is shown to reproduce the deterministic process, while the variance can be expressed as the weighted sum of one-step conditional variances. For the second model, these “innovation variances” will be small for large populations, while for the first and third models their size will depend on the observed variability of, respectively, prediction errors and vital rates. Since it is known empirically that both the latter are quite variable, these models could be expected to yield relatively high prediction variances, and this expectation is confirmed by a numerical example. The first model seems unsatisfactory as demographic theory, while the second does not account for the observed imprecision of population projections. The third model does, however, seem to provide a satisfactory method of estimating prediction variances of population projections.