  Parametric instabilities driven by partially coherent radiation in plasmas
are described by a generalized statistical Wigner-Moyal set of equations,
formally equivalent to the full wave equation, coupled to the plasma fluid
equations. A generalized dispersion relation for Stimulated Raman Scattering
driven by a partially coherent pump field is derived, revealing a growth rate
dependence, with the coherence width $\sigma$ of the radiation field, scaling
with $1/\sigma$ for backscattering (three-wave process), and with
$1/\sigma^{1/2}$ for direct forward scattering (four-wave process). Our results
demonstrate the possibility to control the growth rates of these instabilities
by properly using broadband pump radiation fields.
