Averaging principle for semilinear slow–fast rough partial differential equations

Miaomiao Li, Yunzhang Li, Bin Pei and Yong Xu

Stochastic Processes and their Applications, 2025, vol. 188, issue C

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.

Keywords: Rough path theory; Averaging principle; Rough partial differential equations; Slow–fast system (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104683

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