论文标题
用赫斯特参数$ h \ in（0，\ frac {1} {2} {2} {2}）$的分数布朗运动强制强制的分数波方程的强近似值
Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter $H\in(0,\frac{1}{2})$
论文作者
论文摘要
我们考虑使用高斯噪声的分数随机波方程的时间离散化，这是负相关的。设计和分析随机波方程的时间离散化的主要障碍来自于随机卷积在小部分布朗运动方面的近似。首先，我们通过使用零件的集成和分数布朗运动的协方差函数来讨论随机卷积的平滑特性。然后获得了分数随机波方程的轻度溶液的规律性估计。接下来，我们设计通过零件整合随机卷积的时间离散化。结合了随机三角法和随机卷积的近似，可以实现随机波方程的时间离散化。我们得出时间离散化的错误估计。在某些假设下，本文提出的数值方案的强收敛率可以达到$ \ frac {1} {2}+H $。最后，数值实验说明了数值方案的收敛速率和计算效率。
We consider the time discretization of fractional stochastic wave equation with Gaussian noise, which is negatively correlated. Major obstacles to design and analyze time discretization of stochastic wave equation come from the approximation of stochastic convolution with respect to fractional Brownian motion. Firstly, we discuss the smoothing properties of stochastic convolution by using integration by parts and covariance function of fractional Brownian motion. Then the regularity estimates of the mild solution of fractional stochastic wave equation are obtained. Next, we design the time discretization of stochastic convolution by integration by parts. Combining stochastic trigonometric method and approximation of stochastic convolution, the time discretization of stochastic wave equation is achieved. We derive the error estimates of the time discretization. Under certain assumptions, the strong convergence rate of the numerical scheme proposed in this paper can reach $\frac{1}{2}+H$. Finally, the convergence rate and computational efficiency of the numerical scheme are illustrated by numerical experiments.
