We present a theoretical study on stimulated electronic Raman scattering in neon by resonant excitation with an x-ray free electron laser (XFEL). This study is in support of the recent experimental demonstration [C. Weninger et al., Phys. Rev. Lett. (to be published)] of stimulated x-ray Raman scattering. Focusing the broadband XFEL pulses into a cell of neon gas at atmospheric pressure a strong inelastic x-ray scattering signal in the forward direction was observed, as the x-ray energy was varied across the region of core-excited Rydberg states and the K edge. The broadband and intrinsically incoherent x-ray pulses from the XFEL lead to a rich, structured line shape of the scattered radiation. We present a generalized Maxwell-Liouville–von Neumann approach to self-consistently solve for the amplification of the scattered radiation along with the time evolution of the density matrix of the atomic and residual ionic system. An in-depth analysis of the evolution of the emission spectra as a function of the Raman gain is presented. Furthermore, we propose the use of statistical methods to obtain high-resolution scattering data beyond the lifetime broadening despite pumping with incoherent x-ray pulses.