The paper proposes a new solution to the ill-positioned inverse problems in the mechanical system statistical dynamics using regularization of the random processes by various methods of smoothing their trajectories. It considers cases, where either smoothed white noise or a stationary process with the hidden periodicity is registered at the dynamic system output. In both cases, non-differentiable random processes are present at the system input; their trajectories are smoothed by averaging over the minor intervals or by eliminating features of their amplitude spectra at infinity. As a main example, the paper considers a mechanical system of a device designed to determine probabilistic characteristics of the input kinematic effect on it, it is based on the oscillation protection object registered displacement or on the elastic element deformation.

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