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<p>This paper is devoted to studying the averaging principle for a system of stochastic partial differential equations (SPDEs) that has a slow component driven by fractional Brownian motion (fBm) with a Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H&gt;1/2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>&gt;</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, and a fast component driven by fast-varying diffusion. The optimal orders for the slow component that converges to the solution of the corresponding averaged equation have been obtained by using the Poisson equation method under some appropriate conditions. More precisely, the optimal orders are 1/2 and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((1/2) - \varepsilon ^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <msup> <mi>ε</mi> <mo>∗</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> (for all sufficiently small <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varepsilon ^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ε</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>).</p>

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Convergence Rates in the Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations Driven by Fractional Brownian Motion

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Wujun Lv,
  • Hongsheng Qi,
  • Litan Yan

摘要

This paper is devoted to studying the averaging principle for a system of stochastic partial differential equations (SPDEs) that has a slow component driven by fractional Brownian motion (fBm) with a Hurst parameter \(H>1/2\) H > 1 / 2 , and a fast component driven by fast-varying diffusion. The optimal orders for the slow component that converges to the solution of the corresponding averaged equation have been obtained by using the Poisson equation method under some appropriate conditions. More precisely, the optimal orders are 1/2 and \((1/2) - \varepsilon ^*\) ( 1 / 2 ) - ε ∗ (for all sufficiently small \(\varepsilon ^*\) ε ∗ ).