|
Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 139, Pages 91–103
(Mi into227)
|
|
|
|
Stochastic perturbations of stable dynamical systems: trajectory-wise approach
O. A. Sultanovab a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Peoples Friendship University of Russia, Moscow
Abstract:
We study stochastic perturbations of a dynamical system with a locally stable fixed point. The perturbed system has the form of Ito stochastic
differential equations. We assume that perturbations do not vanish at the equilibrium of the deterministic system. Using the trajectory-wise approach to the analysis of stochastic differential equations, we find restrictions for perturbations under which the stability of the equilibrium is preserved with probability 1.
Keywords:
dynamical system, perturbation, white noise, stochastic differential equation, stability with probability 1.
Citation:
O. A. Sultanov, “Stochastic perturbations of stable dynamical systems: trajectory-wise approach”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139, VINITI, M., 2017, 91–103; Journal of Mathematical Sciences, 241:3 (2019), 340–353
Linking options:
https://www.mathnet.ru/eng/into227 https://www.mathnet.ru/eng/into/v139/p91
|
|