Geodesic
Stochastic Stability of a Dynamical System Perturbed by White Noise
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 130-139

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The effect of small constantly acting random perturbations of white noise type on a dynamical system with locally stable fixed point is studied. The perturbed system is considered in the form of Itô stochastic differential equations, and it is assumed that the perturbation does not vanish at a fixed point. In this case, the trajectories of the stochastic system issuing from points near the stable fixed point exit from the neighborhood of equilibrium with probability $1$. Classes of perturbations such that the equilibrium of a deterministic system is stable in probability on an asymptotically large time interval are described.
Keywords: dynamical system, white noise, stability.
Mots-clés : perturbation 
@article{MZM_2017_101_1_a11,
     author = {O. A. Sultanov},
     title = {Stochastic {Stability} of a {Dynamical} {System} {Perturbed} by {White} {Noise}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {130--139},
     publisher = {mathdoc},
     volume = {101},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a11/}
}
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O. A. Sultanov. Stochastic Stability of a Dynamical System Perturbed by White Noise. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 130-139. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a11/