Exponential stability of solutions for retarded stochastic differential equations without dissipativity

Min Zhu*, Panpan Ren, Junping Li

*Corresponding author for this work

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)2923-2938
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number7
DOIs
Publication statusPublished - 1 Sept 2017
Externally publishedYes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

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

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