论文标题
由高斯和非高斯噪声驱动的时间折叠SPDE的指数积分器和有限元素的强收敛速率
Strong convergence rates of an exponential integrator and finite elements method for time-fractional SPDEs driven by Gaussian and non-Gaussian noises
论文作者
论文摘要
在这项工作中，我们提供了第一个强融合的结果，这是一般二阶半连接的半连续性分数阶进化方程的数值近似值，该方程涉及caputo衍生物在（\ frac 34，1）$的订单$α\中，并由高斯和非高斯和非高斯果实同时使用（在有用的有用）中驱动。这里考虑的高斯噪声是希尔伯特空间有价值的Q-wiener过程，非高斯噪声是通过与Lévy过程相关的补偿泊松随机措施来定义的。线性操作员不是必要的自我偶像。分数随机部分微分方程通过有限元方法在空间中离散，并通过指数积分方案的变体及时地在空间中分配。我们研究了我们完全离散方案的均方误差估计值，结果显示了收敛顺序如何取决于初始数据的规律性和分数衍生物的功率。
In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $α\in(\frac 34, 1)$ and driven by Gaussian and non-Gaussian noises simultaneously more useful in concrete applications. The Gaussian noise considered here is a Hilbert space valued Q-Wiener process and the non-Gaussian noise is defined through compensated Poisson random measure associated to a Lévy process. The linear operator is not necessary self-adjoint. The fractional stochastic partial differential equation is discretized in space by the finite element method and in time by a variant of the exponential integrator scheme. We investigate the mean square error estimate of our fully discrete scheme and the result shows how the convergence orders depend on the regularity of the initial data and the power of the fractional derivative.
