一类高斯随机场非线性泛函的急剧收敛性。

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics Pub Date : 2018-01-01 Epub Date: 2018-11-10 DOI:10.1007/s40304-018-0162-9

Weijun Xu

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引用次数: 4

摘要

给出了一类高斯随机场的三角函数多点相关的一致界的自包含证明。它对应于Hairer和Xu(界面波动模型的大尺度极限)所考虑的一般情况的一个特例。ArXiv电子打印ArXiv:1802.08192, 2018)，但改进了估计。因此，我们建立了一类与更一般函数复合的高斯场的收敛性。这些界和收敛性是建立几个奇异随机偏微分方程的弱普适性的有用成分。

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Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields.

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.

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来源期刊

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.