Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields View Full Text


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Article Info

DATE

2018-12

AUTHORS

Weijun Xu

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 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. More... »

PAGES

509-532

References to SciGraph publications

  • 2014. A Course on Rough Paths, With an Introduction to Regularity Structures in NONE
  • 2014-11. A theory of regularity structures in INVENTIONES MATHEMATICAE
  • 2018-09. Renormalisation of parabolic stochastic PDEs in JAPANESE JOURNAL OF MATHEMATICS
  • 2018-06. Weak universality of dynamical Φ34: non-Gaussian noise in STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS
  • 2017-01. KPZ Reloaded in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2014-05. Nonlinear Fluctuations of Weakly Asymmetric Interacting Particle Systems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1997-02. Stochastic Burgers and KPZ Equations from Particle Systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2019-04. Weak universality for a class of 3d stochastic reaction–diffusion models in PROBABILITY THEORY AND RELATED FIELDS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40304-018-0162-9

    DOI

    http://dx.doi.org/10.1007/s40304-018-0162-9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1109806585

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30931237


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