Scholarlink

<p>Stochastic functional differential equations driven by mixed fractional Brownian motion are often used to describe many systems involving random noise and time delays. In this paper, we give an estimate for the stochastic convolution operator and then give space-time regularity results of the mild solution under the global Lipschitz conditions and linear growth conditions. In particular, when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_984_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="77" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;H&lt;\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>H</mi> <mo>&lt;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>, we use inequality techniques to overcome the singularity of the kernel function of the covariance of fractional Brownian motion. Besides, we propose a fully discrete scheme for this type of equation, which is performed by the spectral Galerkin method in space and the exponential Euler method in time. In the numerical scheme, it is worth noting that the functional terms are discretized by the linear interpolation method. Further, we provide the strong convergence rate of the fully discrete scheme through the obtained regularity results. Finally, our theoretical findings are illustrated with some simulations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Regularity Analysis for SFDEs Driven by Mixed Fractional Brownian Motion and Strong Convergence of a Numerical Scheme

  • 期刊论文

  • 发表日期：

    2025年7月17日

查看全文
  • Xiao-Li Ding,
  • Lanlan Guo,
  • Juan J. Nieto,
  • Yu Gao

摘要

Stochastic functional differential equations driven by mixed fractional Brownian motion are often used to describe many systems involving random noise and time delays. In this paper, we give an estimate for the stochastic convolution operator and then give space-time regularity results of the mild solution under the global Lipschitz conditions and linear growth conditions. In particular, when \(0<H<\frac{1}{2}\) 0 < H < 1 2 , we use inequality techniques to overcome the singularity of the kernel function of the covariance of fractional Brownian motion. Besides, we propose a fully discrete scheme for this type of equation, which is performed by the spectral Galerkin method in space and the exponential Euler method in time. In the numerical scheme, it is worth noting that the functional terms are discretized by the linear interpolation method. Further, we provide the strong convergence rate of the fully discrete scheme through the obtained regularity results. Finally, our theoretical findings are illustrated with some simulations.