Stochastic Perturbations of Stable Dynamical Systems: Trajectory-Wise Approach

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 approach based on consideration of trajectories to the analysis of stochastic differential equations, we find restrictions for perturbations under which the stability of the equilibrium is preserved with probability 1. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Авторы
Издательство
Springer New York LLC
Номер выпуска
3
Язык
Английский
Страницы
340-353
Статус
Опубликовано
Том
241
Год
2019
Организации
  • 1 Institute of Mathematics with Computer Center, Ufa Science Center of the Russian Academy of Sciences, Ufa, Russian Federation
  • 2 Peoples’ Friendship University of Russia, Moscow, Russian Federation
Ключевые слова
34D10; 60H10; 93E15; dynamical system; perturbation; stability with probability 1; stochastic differential equation; white noise
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