Multiple Points of Gaussian Random Fields

2019/11/22 by Robert C. Dalang, Cheuk Yin Lee, Dalang, Robert C. +5 · 3 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1911.09793

openalex publication_date 2019/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.

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• The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold
• On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation
• On the passage times of self-similar Gaussian processes on curved boundaries

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