  Four operating neutrino observatories confirm the long standing discrepancy
between detected and predicted solar neutrino flux. Among these four
experiments the Homestake experiment is taking data for almost 25 years. The
reliability of the radiochemical method for detecting solar neutrinos has been
tested recently by the GALLEX experiment. All efforts to solve the solar
neutrino problem by improving solar, nuclear, and neutrino physics have failed
so far. This may also mean that the average solar neutrino flux extracted from
the four experiments may not be the proper quantity to explain the production
of neutrinos in the deep interior of the Sun. Occasionally it has been
emphasized that the solar neutrino flux may vary over time. In this paper we do
address relations among specific neutrino fluxes produced in the proton-proton
chain that are imposed by the coupled systems of non-linear partial
differential equations of solar structure and kinetic equations by focusing our
attention on a statistical interpretation of selected kinetic equation of
PPII/PPIII branch reactions of the proton-proton chain. A fresh look at the
statistical implications for the outcome of kinetic equations for nuclear
reactions may shed light on recent claims that the $^7$Be-neutrino flux of the
Sun is suppressed in comparison to the pp- and $^8$B neutrino fluxes and may
hint at that the solar neutrino flux is indeed varying over time as shown by
the Homestake experiment.
