Stability of nondissipative systems under persistent random perturbations (Q1938639)

The author studies the stability of the auto-resonance phenomenon under small random perturbations to which known stability results (see [\textit{R. Z. Khas'minskiĭ\,}, Stability of systems of differential equations under random perturbations of their parameters (Russian). Moskva: Izdat. ``Nauka'' (1969; Zbl 0214.15903)]) do not apply. The class of perturbations is restricted by the requirement that, for initial data in a neighborhood of the equilibrium, a global solution exists. It is supposed that perturbations have a majorant, satisfying some conditions described in terms of expectations.