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

Weijun Xu

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arXiv · 1810.03850

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

Weijun Xu

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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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Weijun Xu. 2018-10-09. Sharp convergence of nonlinear functionals of a class of Gaussian random fields. https://arxiv.org/abs/1810.03850

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