Asymptotically Periodic Solution of a Stochastic Differential Equation
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In this paper, we first introduce the concept and properties of \(\omega \)-periodic limit process. Then, we apply specific criteria obtained to investigate asymptotically \(\omega \)-periodic mild solutions of a Stochastic differential equation driven by a Brownian motion. Finally, we give an example to show usefulness of the theoretical results that we obtained in the paper.
KeywordsSquare mean asymptotically periodic Square mean periodic limit Stochastic differential equation Semigroup mild solution
Mathematics Subject Classification34C25 34C27 60H30 34 F05
We thank the anonymous reviewers for their careful reading and many insightful comments and suggestions.
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Conflict of interests
The authors declare that there is no conflict of interest regarding the publication of this paper.