Geodesic
Stability of equilibrium with respect to a white noise
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 112-121

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A system of ordinary differential equations with a local asymptotically stable equilibrium is considered. The problem of stability with respect to a persistent perturbation of the white noise type is discussed. The stability with given estimates is proved on a large time interval with a length of the order of the squared reciprocal magnitude of the perturbation. The proof is based on the construction of a barrier function for the Kolmogorov parabolic equation associated with the perturbed dynamical system.
Keywords: dynamical system; random perturbation; stability; parabolic equation; barrier function. 
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     author = {L. A. Kalyakin},
     title = {Stability of equilibrium with respect to a white noise},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a10/}
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L. A. Kalyakin. Stability of equilibrium with respect to a white noise. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 112-121. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a10/