  We study modulational instability in a fiber system resembling a
dispersion-managed link where the sign of the group-velocity dispersion varies
randomly according to a telegraph process. We find that the instability gain of
stochastic origin converges, for long fiber segment mean length (the inverse of
the transition rate between the two values), to the conventional values found
in a homogeneous anomalous dispersion fiber. For short fiber segments, the gain
bands are broadened and the maximum gain decreases. By employing correlation
splitting formulas, we obtain closed form equations that allow us to estimate
the instability gain from the linearized nonlinear Schr\"odinger equation. We
compare the analytical to the numerical results obtained in a Monte Carlo
spirit. The analysis is proven to be correct not only for a fluctuating
group-velocity dispersion, but also including fourth-order dispersion (both
constant or varying according to a synchronous or independent telegraph
process). These results may allow researchers to tailor and control
modulational instability sidebands, with applications in telecommunications and
parametric photon sources.
