Maxima and minima of homogeneous Gaussian random fields over continuous time and uniform grids

2019/03/28 by Yingyin Lu, Lu, Yingyin, Zuoxiang Peng +1
Economics, Econometrics and Finance · Mathematics · #60G15 #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60G15 #msc:60G70

paper · pdf · doi:10.48550/arxiv.1903.11740

24 pages

arxiv created 2019/03/28 · openalex publication_date 2019/03/28 · arxiv updated 2019/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, for centered homogeneous Gaussian random fields the joint limiting distributions of normalized maxima and minima over continuous time and uniform grids are investigated. It is shown that maxima and minima are asymptotic dependent for strongly dependent homogeneous Gaussian random field with the choice of sparse grid, Pickands' grid or dense grid, while for the weakly dependent Gaussian random field maxima and minima are asymptotically independent.

Citations

• On excursion sets, tube formulas and maxima of random fields

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