We describe a theoretical framework to analyze the dynamics of gene expression with stochastic bursts beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations. We propose an expansion of the master equation for the joint process. The resulting coarse-grained model is a reduced system describing only the protein population while fully accounting for the effects of discrete and fluctuating mRNA population. Closed form expressions for the stationary distribution of the protein population and mean first-passage times of the coarse-grained model are derived. Large-scale Monte Carlo simulations show that the analysis accurately describes the individual-based process accounting for mRNA population in contrast to the failure of commonly proposed diffusion-type models. This is joint work with Yen Ting Lin (Los Alamos). Speaker(s): Charles Doering (University of Michigan)