Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations
Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations
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DOI：
10.1007/s40072-022-00236-y
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Ioannis Gasteratos;M. Salins;K. Spiliopoulos
中科院分区：
文献类型：
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作者：
Ioannis Gasteratos;M. Salins;K. Spiliopoulos
本文的目的是研究慢速分量和快速分量在时间尺度上分离且慢速分量中噪声较小的随机反应扩散方程组的适度偏差原理。基于无限维弱收敛方法和相关随机控制参数，当小噪声和时间尺度分离参数消失时，我们获得了不同状态下适度偏差率函数的精确形式。由于问题的无限维而出现的许多问题在其有限维对应物中完全不存在。与相应的大偏差原则相比，中等偏差缩放需要更精细的方法来建立紧密性并正确识别潜在受控问题的限制行为。后者涉及希尔伯特空间上相关椭圆柯尔莫哥洛夫方程解的正则性质以及有限维近似参数。
The goal of this paper is to study the moderate deviation principle for a system of stochastic reaction–diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak convergence methods in infinite dimensions and related stochastic control arguments, we obtain an exact form for the moderate deviations rate function in different regimes as the small noise and time-scale separation parameters vanish. Many issues that appear due to the infinite dimensionality of the problem are completely absent in their finite-dimensional counterpart. In comparison to corresponding large deviation principles, the moderate deviation scaling necessitates a more delicate approach to establishing tightness and properly identifying the limiting behavior of the underlying controlled problem. The latter involves regularity properties of a solution of an associated elliptic Kolmogorov equation on Hilbert space along with a finite-dimensional approximation argument.