Erosion and deposition rates estimated from the stratigraphic record frequently exhibit a power-law dependence on measurement interval. This dependence can result from a power-law distribution of stratigraphic hiatuses. By representing the stratigraphic filter as a stochastic process called a reverse ascending ladder, we describe a likely origin of power-law hiatuses, and thus, rate scaling. While power-law hiatuses in certain environments can be a direct result of power-law periods of stasis (no deposition or erosion), they are more generally the result of randomness in surface fluctuations irrespective of mean subsidence or uplift. Autocorrelation in fluctuations can make hiatuses more or less heavy-tailed, but still exhibit power-law characteristics. In addition we show that by passing stratigraphic data backward through the filter, certain statistics of surface kinematics from their formative environments can be inferred.