Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields.
Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields.
复制标题
一类高斯随机场的非线性泛函的急剧收敛。
DOI：
10.1007/s40304-018-0162-9
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发表时间：
2018
影响因子：
0.9
通讯作者：
Xu W
中科院分区：
文献类型：
--
作者：
Xu W
给出了一类高斯随机场三角函数多点相关一致界的完备证明。它对应于Hairer和Xu（界面波动模型的大尺度极限）中所考虑的一般情况的特殊情况。ArXiv电子打印 1802.08192 ，2018年），但估计有所改善。作为结果，我们建立了一类高斯场与更一般的功能复合的收敛性。这些边界和收敛性是有用的成分，建立弱的普遍性的几个奇异随机偏微分方程。
We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in Hairer and Xu (large-scale limit of interface fluctuation models. ArXiv e-prints arXiv:1802.08192 , 2018), but with improved estimates. As a consequence, we establish convergence of a class of Gaussian fields composite with more general functions. These bounds and convergences are useful ingredients to establish weak universalities of several singular stochastic PDEs.