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<p>This paper investigates stochastic averaging principle for a class of mixed slow-fast stochastic differential equations driven simultaneously by a multidimensional standard Brownian motion and a multidimensional fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2024_368_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">\(1/2&lt;H&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mo>&lt;</mo> <mi>H</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The stochastic averaging principle shows that the slow component strongly converges to the solution of the corresponding averaged equations under a weaker condition than the Lipschitz one.</p>

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Mixed slow-fast stochastic differential equations: Averaging principle result

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Shitao Liu

摘要

This paper investigates stochastic averaging principle for a class of mixed slow-fast stochastic differential equations driven simultaneously by a multidimensional standard Brownian motion and a multidimensional fractional Brownian motion with Hurst parameter \(1/2<H<1\) 1 / 2 < H < 1 . The stochastic averaging principle shows that the slow component strongly converges to the solution of the corresponding averaged equations under a weaker condition than the Lipschitz one.