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Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions

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Abstract

In this paper, we are concerned with multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index \(H>\frac{1}{2}\)) and standard Brownian motion, simultaneously. Our aim is to establish a large deviation principle for the multi-scale distribution-dependent stochastic differential equations. This is done via the weak convergence approach and our proof is based heavily on the fractional calculus.

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Acknowledgements

The authors would like to thank the referees for their insightful comments and suggestions which have led us to improve the presentation of the paper. The researches of Guangjun Shen and Huan Zhou were supported by the National Natural Science Foundation of China (12071003). The research of Jiang-Lun Wu was partly supported by the UIC Start-up Research Fund (No. UICR0700072-24).

Funding

Guangjun Shen and Huan Zhou were supported by the Natural Science Foundation of China (12071003).

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Author notes

  1. Jiang-Lun Wu

    Present address: Faculty of Science and Technology, BNU-HKBU United International College, Zhuhai, 519087, China

Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241002, China

    Guangjun Shen & Huan Zhou

  2. Department of Mathematics, Computational Foundry, Swansea University, Swansea, SA1 8EN, UK

    Jiang-Lun Wu

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  1. Guangjun Shen
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Contributions

GS was involved in the conceptualization and proving and writing for the original draft. JLW contributed by proving, reviewing, editing and coordinating. HZ contributed to methodology and proving for the original draft. All authors reviewed the manuscript.

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Correspondence to Jiang-Lun Wu.

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Shen, G., Zhou, H. & Wu, JL. Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions. J. Evol. Equ. 24, 35 (2024). https://doi.org/10.1007/s00028-024-00960-z

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