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Exponential stability of solutions for retarded stochastic differential equations without dissipativity

  • * Corresponding author: Min Zhu

    * Corresponding author: Min Zhu 
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  • 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.

    Mathematics Subject Classification: 60H10, 39B82, 60H30, 37H10.

    Citation:

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