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On the Almost Sure Stability of Dynamical Systems with Respect to White Noise

Abstract

We consider a system of ordinary differential equations possessing an asymptotically stable equilibrium position and examine the stability of this equilibrium under permanent stochastic whitenoise-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.

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Correspondence to O. A. Sultanov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 152, Mathematical Physics, 2018.

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Cite this article

Sultanov, O.A. On the Almost Sure Stability of Dynamical Systems with Respect to White Noise. J Math Sci 252, 242–246 (2021). https://doi.org/10.1007/s10958-020-05157-6

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Keywords and phrases

  • dynamical system
  • perturbation
  • white noise
  • stability

AMS Subject Classification

  • 93E15
  • 34D10
  • 60H10