TY - JOUR

T1 - Stochastic stability of a dynamical system perturbed by white noise

AU - Sultanov, O. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - dynamical system

KW - perturbation

KW - stability

KW - white noise

UR - http://www.scopus.com/inward/record.url?scp=85015666909&partnerID=8YFLogxK

U2 - 10.1134/S0001434617010151

DO - 10.1134/S0001434617010151

M3 - Article

AN - SCOPUS:85015666909

VL - 101

SP - 149

EP - 156

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -