A convergence model in which wealth accumulation is subject to i.i.d. random shocks is examined. The accumulation function shows that kt+1 - wealth t+1 - would be given kt and with no shock. It has a positive slope, but its concavity or convexity is indeterminate. The focus is the ergodic distribution of wealth. This distribution satisfies a Fredholm integral equation. The ergodic distribution can be characerized in some respects by direct analysis of the stochastic process governing wealth accumulation and by use of the Fredholm equation without solution. Multiple local maxima in the ergodic distribution cannot be ruled out.