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System of differential equations describing the initial stage of the captureof oscillatory systems into the parametric autoresonance is considered. Ofspecial interest are solutions whose amplitude increases without bound withtime. The possibility of capture the system into the autoresonance is relatedwith the stability of such solutions. We study the stability of autoresonantsolutions with respect to persistent perturbations of white noise type, and weshow that under certain conditions on the intensity of the noise, the captureinto parametric autoresonance is preserved with probability tending to one.

Capture into parametric autoresonance in the presence of noise