  We present a stochastic theory of linewidths for magnetization oscillations
in spin-valve structures driven by spin-polarized currents. Starting from a
nonlinear oscillator model derived from spin-wave theory, we derive Langevin
equations for amplitude and phase fluctuations due to the presence of thermal
noise. We find that the spectral linewidths are inversely proportional to the
spin-wave intensities with a lower bound that is determined purely by
modulations in the oscillation frequencies. Reasonable quantitative agreement
with recent experimental results from spin-valve nanopillars is demonstrated.
