Exponential stability of solutions for retarded stochastic differential equations without dissipativity

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Original languageEnglish
Pages (from-to)2923-2938
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series B
Issue number7
Publication statusPublished - 1 Sept 2017
Externally publishedYes


This work focuses on a class of retarded stochastic differential equations that need not satisfy dissipative conditions. The principle technique of our investigation is to use variation-of-constants formula to overcome the difficulties due to the lack of the information at the current time. By using variation-of-constants formula and estimating the diffusion coefficients we give sufficient conditions for p-th moment exponential stability, almost sure exponential stability and convergence of solutions from different initial value. Finally, we provide two examples to illustrate the effectiveness of the theoretical results.

Research Area(s)

  • Almost sure exponential stability, Dissipativity, Exponential stability, Retarded stochastic differential equations, Variation-of-constants formula

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