The problem of parametric instabilities in the presence of space‐time fluctuation in homogeneous or inhomogeneous plasmas can be cast into the problem of finding an effective HamiltonianHeffof the linear stochastic equation. For the Kubo–Anderson–random‐phase model (RPM) [J. Math. Phys.15, 524 (1974); Phys. Rev. Lett.29, 565 (1972); J. Phys. Soc. Jpn.9, 316 (1954)],Heffis generally found to be of the formH0+&Dgr;&ohgr;H1, whereH0represents all the coherent effects and &Dgr;&ohgr;H1represents the finite bandwidth modification. It is shown thatH1is a trivial constant matrix for all parametric processes. A method called frame transformation is introduced to treat all kinds of group velocities in a unified fashion. The theory can be used to calculate average amplitude as well as average power. Importantly, the theory is not limited to wide bandwidths.