Strong Law of Large Numbers for Functionals of Random Fields With\n Unboundedly Increasing Covariances

2020/11/09 by Illia Donhauzer, Donhauzer, Illia, Andriy Olenko +3
Decision Sciences · Economics, Econometrics and Finance · #60F15 #60G60 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2011.04874

openalex publication_date 2020/11/09 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The paper proves the Strong Law of Large Numbers for integral functionals of\nrandom fields with unboundedly increasing covariances. The case of functional\ndata and increasing domain asymptotics is studied. Conditions to guarantee that\nthe Strong Law of Large Numbers holds true are provided. The considered\nscenarios include wide classes of non-stationary random fields. The discussion\nabout application to weak and long-range dependent random fields and numerical\nexamples are given.\n

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