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A Support Theorem for Stochastic Differential Equations Driven by a Fractional Brownian Motion

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Abstract

In this paper we prove a support theorem for a class of Itô–Volterra equations related to the fractional Brownian motion. The simplified method developed by Millet and Sanz-Solé plays an important role.

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Acknowledgements

The authors are very grateful to Professor Jicheng Liu for his encouragement and help.

The authors also acknowledge the support provided by key scientific research project plans of Henan province advanced universities No.21A110011 and NSFs of China Nos.11971154 and 11901154.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Jie Xu & Yanhua Sun

  2. College of Mathematics and Information Science, Henan University of Economics and Laws, Zhengzhou, 450002, Henan, People’s Republic of China

    Jie Ren

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  1. Jie Xu
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  2. Yanhua Sun
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  3. Jie Ren
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Correspondence to Jie Xu.

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Xu, J., Sun, Y. & Ren, J. A Support Theorem for Stochastic Differential Equations Driven by a Fractional Brownian Motion. J Theor Probab 36, 728–761 (2023). https://doi.org/10.1007/s10959-022-01186-w

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  • DOI: https://doi.org/10.1007/s10959-022-01186-w

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