论文标题
部分可观测时空混沌系统的无模型预测
Mittag--Leffler Euler integrator and large deviations for stochastic space-time fractional diffusion equations
论文作者
论文摘要
随机时空分数扩散方程经常出现在非均匀培养基中热传播的建模中。在本文中，我们首先研究了一类随机时空分数扩散方程的leffler Euler集成仪，该方程是通过为时间分数积分开发有用的分解方式而获得的超级连锁顺序。在这里，开发的分解方式是处理解决方案操作员的奇异性的关键。此外，我们根据弱收敛方法研究了基础方程式及其Mittag的Freidlin-Wentzell类型的大偏差原理。特别是，我们证明了Mittag-Leffler Euler Integrator $γ$ - 对基础方程的大偏差率函数。
Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper, we firstly investigate the Mittag--Leffler Euler integrator of a class of stochastic space-time fractional diffusion equations, whose super-convergence order is obtained by developing a helpful decomposition way for the time-fractional integral. Here, the developed decomposition way is the key to dealing with the singularity of the solution operator. Moreover, we study the Freidlin--Wentzell type large deviation principles of the underlying equation and its Mittag--Leffler Euler integrator based on the weak convergence approach. In particular, we prove that the large deviation rate function of the Mittag--Leffler Euler integrator $Γ$-converges to that of the underlying equation.
