Stability of equilibrium with respect to white noise |
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Authors: | L A Kalyakin |
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Institution: | 1.Institute of Mathematics with Computing Center,Ufa Research Center of the Russian Academy of Sciences,Ufa,Russia |
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Abstract: | 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. Stability with given bounds is proved on a large time interval with length of the order of the squared inverse perturbation amplitude. The proof is based on the construction of a barrier function for the parabolic Kolmogorov equation associated with the perturbed dynamical system. |
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