Fiber dispersion plays a significant role in spectral broadening of incoherent continuous-wave light. We develop a self-consistent stochastic model for spectral broadening of incoherent continuous-wave light through nonlinear wave mixing and apply this model to numerical simulations of spectral broadening in a continuous-wave fiber Raman laser. The results of these numerical simulations agree very well with carefully conducted laboratory measurements. Under a wide range of operating conditions, these numerical simulations also exhibit striking features, such as damped oscillatory spectral broadening (during the initial stages of propagation) and eventual convergence to a stationary, steady-state spectral distribution at sufficiently long propagation distances. We analyze the important role of fiber dispersion in such phenomena. We also derive an analytical rate equation expression for spectral broadening, whose numerical evaluation is far less computationally intensive than the fully stochastic simulation, and a mathematical criterion for the applicability of this analytical expression.