In previous work, we have developed mathematical tools for the analysis of single-cell gene expression data from population snapshots, and an inference algorithm for the estimation of stationary statistics of promoter activation. In this work, we address the inference problem in the nonstationary case of modulated processes. This is of special relevance to control scenarios, where an exogenous input modulates the time evolution of promoter activation. We provide an effective method for the computation of the output statistics of a reaction network with a nonstationary, causal input process of modulated form. Based on this we devise and demonstrate an algorithm for the reconstruction of the promoter (input) process statistics from snapshot data.