A standard neoclassical convergence model in which wealth accumulation is subject to random shocks is examined. The focus is on the limiting, or ergodic, distribution of wealth. This distribution satisfies a Fredholm integral equation. Direct mathematical solution is not possible. However results obtained characterize the limiting distribution of the logarithms of wealth values as a single-peaked distribution. It is asymmetric with the left-hand tail more heavily weighted. It follows that models which treat wealth transition as purely random lead to qualitatively different outcomes from those implied by the neoclassical convergence model augmented by random shocks.