  System of differential equations describing the initial stage of the capture
of oscillatory systems into the parametric autoresonance is considered. Of
special interest are solutions whose amplitude increases without bound with
time. The possibility of capture the system into the autoresonance is related
with the stability of such solutions. We study the stability of autoresonant
solutions with respect to persistent perturbations of white noise type, and we
show that under certain conditions on the intensity of the noise, the capture
into parametric autoresonance is preserved with probability tending to one.
