描述由分片状布朗薄片噪音驱动的超扩散和亚扩散之间竞争的模式的正规化解决办法的最佳趋同 (Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise)

正则化项 · 噪声 · 优化器 · Integration · MoDELS ·

2022 年 9 月 2 日

Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise

翻译：描述由分片状布朗薄片噪音驱动的超扩散和亚扩散之间竞争的模式的正规化解决办法的最佳趋同

Jing Sun,Daxin Nie,Weihua Deng

from arxiv, 22 pages, 1 figure

Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise. Based on the obtained regulization result of the solution by using the properties of Mittag-Leffler function and the regularized noise by Wong-Zakai approximation, we make full use of the regularity of the solution operators to achieve optimal convergence of the regularized solution. The spectral Galerkin method and the Mittag-Leffler Euler integrator are respectively used to deal with the space and time operators. In particular, by contour integral, the fast evaluation of the Mittag-Leffler Euler integrator is realized. We provide complete error analyses, which are verified by the numerical experiments.

翻译：超扩散和次扩散是自然界反常扩散的两种典型类型。在这项工作中,我们讨论了描述由分片状布朗板块噪音驱动的超扩散和次扩散之间的竞争的模型数字方案。根据溶液获得的调制结果,我们利用Mittag-Leffler功能的特性和Wong-Zakai近似法的固定噪音,充分利用溶液操作员的常规性,实现正规化溶液的最佳趋同。光谱加列金方法和Mittag-Leffler Euler合成器分别用来处理空间和时间操作器。特别是,通过轮廓集,实现了对Mittag-Leffler Euler集成器的快速评估。我们提供了完整的错误分析,这些分析经过数字实验核实。