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Averaging principle for semilinear slow–fast rough partial differential equations

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  • Li, Miaomiao
  • Li, Yunzhang
  • Pei, Bin
  • Xu, Yong

Abstract

In this paper, we investigate the averaging principle for a class of semilinear slow–fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random γ-Hölder rough path for some γ∈(1/3,1/2), while the fast component is driven by an Itô-type Brownian rough path. Using controlled rough path theory and the classical Khasminskii’s time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology.

Suggested Citation

  • Li, Miaomiao & Li, Yunzhang & Pei, Bin & Xu, Yong, 2025. "Averaging principle for semilinear slow–fast rough partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001243
    DOI: 10.1016/j.spa.2025.104683
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    References listed on IDEAS

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    1. Wang, Ruifang & Xu, Yong & Yue, Hongge, 2022. "Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 182(C).
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    4. Hong, Wei & Li, Shihu & Liu, Wei, 2020. "Asymptotic log-Harnack inequality and applications for SPDE with degenerate multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 164(C).
    5. Fu, Hongbo & Wan, Li & Liu, Jicheng, 2015. "Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3255-3279.
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