  We study the effect of random matter density fluctuations in the sun on
resonant neutrino conversion in matter by solving numerically the evolution
equation for the neutrino system including the full effect of the random matter
density fluctuations of given amplitude and correlation length. In order to
establish the possible effect on the MSW solutions to the solar neutrino
problem we perform a global analysis of all the existing observables including
the measured total rates as well as the Super-Kamiokande measurement on the
time dependence of the event rates during the day and night and the recoil
electron energy spectrum. We find the effects of random noise to be larger for
small mixing angles and they are mostly important for correlation lengths in
the range few 100 km $\lesssim L_0\lesssim$ few 1000 km. They can be understood
as due to a parametric resonance occuring when the phase acquired by the
oscillating neutrino state on one fluctuation length L_0 is a multiple of
2$\pi$. We find that this resonant parametric condition is mainly achieved for
low energy neutrinos such as the pp-neutrinos and therefore its effect is
mostly seen on the total event rates while the other Super-Kamiokande
observables are very marginally sensitive to the presence of noise due to the
higher energy threshold.
