Asymptotic approximations and numerical computations are used to estimate the accuracy of the diffusion approximation for the expected time to extinction for some stochastic processes. The results differ for processes with a continuant transition matrix (e.g. a birth and death process), and those with a noncontinuant transition matrix (e.g. a non-linear branching process). In the latter case, the diffusion equation does not hold near the point of exit. Consequently, high-order corrections do not result in substantial improvement over the diffusion approximation.
