由分数布朗运动驱动的半线性随机发展方程的Weyl伪概周期型解
Weyl Pseudo Almost Periodic Type Solutions to Semilinear Stochastic Evolution Equations Driven by Fractional Brownian Motion
- Virginia Military Institute (VMI)（弗吉尼亚军事学院）
- Faculty of Technical Sciences, University of Novi Sad（诺维萨德大学技术科学学院）
- Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje（斯科普里圣西里尔和圣美多德大学土木工程学院数学与信息系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究由分数布朗运动驱动的半线性随机发展方程的Weyl概周期型解，通过Hölder连续性条件克服协方差不可积性，并给出随机抛物方程示例验证结果。
AI中文摘要：
本文分析了一类由Hurst指数$H<1/2$的双边分数布朗运动驱动的可分Hilbert空间中的半线性发展方程的平方均值Weyl概周期解和平方均值Weyl双测度伪概周期解。由于$H<1/2$时协方差密度的不可积性，需要对扩散系数施加Hölder连续性条件。一个涉及随机抛物方程的示例说明了所得结果的适用性。
英文摘要：
In this paper, we analyze square-mean Weyl almost periodic solutions and square-mean Weyl double-measure pseudo almost periodic solutions for a class of semilinear evolution equations in separable Hilbert spaces driven by two-sided fractional Brownian motion with Hurst index $H<1/2$. Due to the non-integrability of covariance density for $H<1/2$, a Hölder-continuity condition on the diffusion coefficient is required. An illustrative example involving a stochastic parabolic equation demonstrates the applicability of obtained results.
