论文标题
对于由分数高卢噪声驱动的分数扩散方程方案方案方案方案方案的强收敛顺序
Strong convergence order for the scheme of fractional diffusion equation driven by fractional Gaussion noise
论文作者
论文摘要
分数高斯噪声以远程依赖性模型。当Hurst索引$ H> 1/2 $时，它具有正相关，反映了持续的自相关结构。本文研究了用于解决由分数高斯噪声驱动的随机分数扩散方程的数值方法。使用操作员理论方法，我们介绍了轻度溶液的规律性估计值和完全离散的方案，并及时及时具有有限的元素近似值。 $ \ MATHCAL {O}（τ^{H-ρα}）$收敛率和$ \ Mathcal {o}（H^{\ min（2,2-2ρ，\ frac {h}α）} $在空间中获得噪声和噪声$之间的关系$之间的关系$ quointity的关系$ iS a $ quotion pame n a $ $α\ in（0,1）$。最后，进行数值实验以支持理论结果。
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving stochastic fractional diffusion equation driven by fractional Gaussian noise. Using the operator theoretical approach, we present the regularity estimate of the mild solution and the fully discrete scheme with finite element approximation in space and backward Euler convolution quadrature in time. The $\mathcal{O}(τ^{H-ρα})$ convergence rate in time and $\mathcal{O}(h^{\min(2,2-2ρ,\frac{H}α)})$ in space are obtained, showing the relationship between the regularity of noise and convergence rates, where $ρ$ is a parameter to measure the regularity of noise and $α\in(0,1)$. Finally, numerical experiments are performed to support the theoretical results.
