An invariance principle for stationary random fields under Hannan's condition

2014/03/18 by Dalibor Volný, Volný, Dalibor, Yizao Wang +1
Decision Sciences · Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.4613

openalex publication_date 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an invariance principle for a general class of stationary random fields indexed by \mathbb Z^d, under Hannan's condition generalized to \mathbb Z^d. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and particularly we require only finite second moment.

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