Sharp convergence of nonlinear functionals of a class of Gaussian random fields

2018/10/09 by Xu, Weijun
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.03850

Abstract

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-Xu], 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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