Geodesic
On the Almost Sure Stability of Dynamical Systems with Respect to White Noise
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 120-124.

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We consider a system of ordinary differential equations possessing an asymptotically stable equilibrium position and examine the stability of this equilibrium under permanent stochastic white-noise-type perturbations. The perturbed system is considered in the form of Stratonovich stochastic differential equations. We also describe restrictions on the parameters of perturbations that guarantee the trajectory-wise stability of the equilibrium with probability $1$.
Keywords: dynamical system, white noise, stability.
Mots-clés : perturbation 
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O. A. Sultanov. On the Almost Sure Stability of Dynamical Systems with Respect to White Noise. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 120-124. http://geodesic.mathdoc.fr/item/INTO_2018_152_a10/

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