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The gain and reflectivity of the stimulated Brillouin scattering (SBS) process used as a Stokes-wave generator are shown theoretically to be independent of the mode structure of the pump laser provided that the pump-laser mode spacing exceeds the Brillouin linewidth and that the laser coherence length exceeds the characteristic gain length of the SBS process. Under the same set of conditions, the gain of an SBS amplifier is found to depend on the degree of correlation between the laser and Stokes fields. However, due to nonlinear coupling, these two fields become correlated within several characteristic gain lengths, and the subsequent propagation of the two fields is governed by the same set of equations that apply for the case of a single-mode pump laser. These theoretical predictions are tested experimentally for an SBS generator using acetone, carbon disulfide, and methanol as the Brillouin-active media, and the results are in full agreement with the theoretical predictions.