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Existence and uniqueness for solutions of mixed stochastic delay differential equations

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Abstract

We consider a class of one-dimensional mixed stochastic delay differential equations driven by Brownian motions and fractional Brownian motions with Hurst parameter \(H\in (\frac{1}{2},1).\) A existence and uniqueness result is proved by using a contraction principle and some priori estimations. Some previous works are generalized and improved partially.

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Acknowledgements

This research is supported by Project of Department of Education of Guangdong Province (No.2018KTSCX072) and Guangdong University of Finance & Economics, Big data and Educational Statistics Application Laboratory (No.2017WSYS001). The authors are very grateful to Professor Guiwu Hu for his supports and encouragement. We also thanks the referees for their valuable remarks and suggestions which led to improvement of the paper.

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Correspondence to Weiguo Liu.

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This research is supported by Project of Department of Education of Guangdong Province (No.2018KTSCX072) and Guangdong University of Finance and Economics, Big data and Educational Statistics Application Laboratory (No.2017WSYS001).

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Liu, W., Yu, Q. & Zhang, X. Existence and uniqueness for solutions of mixed stochastic delay differential equations. Res Math Sci 8, 37 (2021). https://doi.org/10.1007/s40687-021-00275-2

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