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<p>In this work, we establish a strong averaging principle for a class of McKean–Vlasov stochastic partial differential equations (SPDEs) with two-timescale structures, driven by Lévy noise. By employing Khasminskii’s time discretization method in combination with a variational approach, we prove that the slow component converges strongly to the solution of the corresponding averaged equation. Furthermore, we derive explicit rates of convergence. The main results can be applied to a set of nonlinear McKean–Vlasov SPDEs, including the stochastic porous medium equation, the stochastic <i>p</i>-Laplace equation, as well as McKean–Vlasov stochastic differential equations.</p>

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Averaging Principle for Multi-scale McKean–Vlasov SPDEs Driven by Lévy Noise

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Jinming Li,
  • Shihu Li

摘要

In this work, we establish a strong averaging principle for a class of McKean–Vlasov stochastic partial differential equations (SPDEs) with two-timescale structures, driven by Lévy noise. By employing Khasminskii’s time discretization method in combination with a variational approach, we prove that the slow component converges strongly to the solution of the corresponding averaged equation. Furthermore, we derive explicit rates of convergence. The main results can be applied to a set of nonlinear McKean–Vlasov SPDEs, including the stochastic porous medium equation, the stochastic p-Laplace equation, as well as McKean–Vlasov stochastic differential equations.